Tanjung Puting National Park in Borneo provides a haven for endangered orangutans — and a place for close encounters with them. (Hugh Biggar)

The swampy heat swaddles everything like a wet diaper. The coffee-colored Sekonyer River looks tempting to cool off in, but then there are the crocodiles and the water snakes. Somewhere out there, too, are rumors of headhunters — and not the K Street kind.

Instead, my family and I decide to kick back and let the orangutans in Borneo’s Tanjung Puting National Park come to us.

The park is one of the best places in the world to see the endangered orangutan in the wild. With South Asia’s tropical forests rapidly disappearing, particularly in Borneo, it’s also one the of only places where you can still see the great apes in their natural habitat.

To reach the park, we fly to Indonesia’s Central Kalimantan province from Jakarta, then take an old African Queen-style wooden boat from the port of Kumai on the Java Sea. We plop ourselves in deck chairs as the boat slowly putt-putts away from Kumai’s fishing shacks, cargo sheds and bright blue mosque, wheezes past freighters and canoes, and finally enters a channel leading to the jungle. Here, an unexpected billboard featuring a large picture of a big-eyed orangutan announces the entrance to the park.

Other than in the picture, though, the orangutans are initially hard to spot. Although the rain forest presses close on both sides of the boat, the apes stay hidden.

Our guide helpfully instructs us to look for swaying branches up in the canopy and for nests made of sticks: This is because orangutans are tree-dwellers, in fact the largest tree-dwelling mammals in the world.

We also learn to look in front of the boat, rather than to the side, and soon we spot moms with babies firmly attached swinging from tree branch to tree branch or munching contentedly on fruit. At ground level, I see solitary males, with their telltale large, leathery cheek pads, along the reedy banks. Most are drinking from the river or scavenging for food. Scientists have found that some of the park’s apes use sticks to spear fish, but the orangutans near us are stickless.

I spot one big male squatting in the mud, oblivious to the boat but riveted by a stray soda can. Slowly, he turns the can end over end, trying to divine its shiny purpose. Then, finding the top, he pops open the tab and, to his considerable surprise, sprays himself in the face. Those opposable thumbs can be a mixed blessing, I suppose.

Farther along, less shy orangutans, both moms with babies and solitary males, watch the boat from branches close to the shore. Our guide calls to the animals, whistling and making kissing sounds. The orangutans remain silent but cautiously swing closer to the boat. A few venture to waterside branches, although the park discourages visitors from getting too close for safety (the 250- to 300-pound males can be dangerously unpredictable) and health reasons.

I tentatively hold out a banana to one mom and, standing face to face with her, suddenly feel an easy kinship with the great ape. Not surprising, since they share 97 percent of our DNA. Our guide tells us that the word “orangutan” derives from a Malay word meaning “forest man.”

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Gibbons, macaques and big-bellied, big-nosed proboscis monkeys (which locals call Dutch monkeys after the island’s former colonial overlords) also wait to join in on the banana mother lode and peer curiously from nearby trees. Somewhere in the forest, too, are clouded leopards, sun bears and pygmy elephants, but these animals are too savvy to let us see them, and for good reason. Humans haven’t been so kind to the rain forest and its denizens in recent decades.

Today, orangutans are squeezed into diminishing rain forests in Sumatra and Borneo, an island that Indonesia shares with Malaysia and Brunei. The global population is roughly 55,000, down from about 300,000 a century ago, when the apes lived throughout the swampy jungles of Southeast Asia, including in Southern China.

In Borneo, wildfires, logging and palm oil plantations have helped wipe out most of the orangutans’ natural habitat. Indonesia, which boasts the most tropical forests in the world after Brazil, continues to lose millions of forest acres each year, thanks to the rising popularity of palm oil as a cooking oil and biofuel. The forests are burned and the peat swamps drained, and palm trees planted instead.

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Big palm oil plantations surround Tanjung Puting, trapping the orangutans here and preventing them from traveling to other nearby rain forests and swamps. But the park is undeniably a sanctuary for those orangutans left in Borneo and for those being reintroduced into the wild, thanks especially to the work of Birute Mary Galdikas. A protege of anthropologist Louis Leakey, Galdikas (featured in the recent documentary “Born to Be Wild”) arrived at the park 40 years ago and never left. She has established the conservation organization Orangutan Foundation International and dedicated her life to studying and helping orangutans such as Siswi.

We meet Siswi after stopping at the park headquarters, Camp Leakey, where we stretch our legs and breathe in the fresh air after spending the night on a deck heavy with mosquitoes and the smell of kerosene, diesel, bug spray and the onboard toilet.

We follow a bamboo boardwalk over a peat swamp, past a linebacker-size male orangutan in the grass who eyes us warily, and into the heart of the camp. Here, among a cluster of small bungalows, smack in the middle of the trail, the camp grandmother lies on her back, a lazy grin on her face, holding her feet over her head with her hands in what could be a yoga position — upward-facing primate, perhaps.

Siswi is the resident elder, mascot and clown. In her late 30s, she has three grandchildren, about right for an animal that gives birth every eight to 15 years — a long gap between offspring that adds to orangutans’ vulnerability to extinction.

We sidestep Siswi, who doesn’t budge, and continue down the trail toward the feeding station in the jungle. Our guide calls ahead with his whistles and kisses to let the apes know that we are coming, and the trees rustle with macaques and gibbons. Nearby, a wild boar roots in the grass.

A mile or so into the rain forest, we arrive at the station, where orangutan moms and babies are sitting calmly on a wooden platform. Two other visitors occupy nearby benches, watching as the orangutans feast on piles of blackish bananas and milk. Less social apes slide down from the trees and grab a handful of fruit before heading back up into the canopy.

We join the other visitors on the benches, fan ourselves with leaves and dive out of the way when a large male orangutan rumbles down the jungle path and swings up over the benches and onto the platform.

For these apes at least, life seems good, despite the greater troubles facing the species.

For certain other apes — namely us — the heat of the midday sun makes us wonder how these thickly furred creatures keep cool. We’re barely hanging in there as the humidity rises, and after half an hour, drooping, we reluctantly head back to the camp. I also pause to remove a leech from my ankle and to inspect a plant slowly devouring an insect.

At Camp Leakey, we stop briefly to cool off on wooden benches in the shade and to visit a small museum in an old bungalow that features faded photos of camp apes, including their names and lineages, and a few natural history displays. I stretch my arms out at one exhibit and realize that I don’t come close to the typical male orangutan wingspan of eight feet. Perhaps the Washington Wizards should send out a scout.

Outside the bungalow, I take a seat in the shade and douse myself with water from my bottle. Siswi sidles up with a sly look on her face.

Still ahead this afternoon are a visit to a fishing village of the local Dayak people, just past an outlaw mid-river gold-mining operation, where men turn drills by pedaling stationary bikes, and then a side trip into the swamps in canoes low enough in the dark water to give us an unnerving crocodile’s-eye view of the world. Tomorrow, we head back to Kumai and then to Jakarta.

But for now, it’s just me and Siswi in the shade. She seems to have a better idea for my water bottle and holds out her hand for it. I forget about the heat, the bugs and the leeches. Siswi and I look each other in the eye, and suddenly it’s not clear which of us is giving the other something to take home.

Biggar is a writer based in Washington and California.