Ponte Vecchio, Florence, Italy (Yury Prokopenko/GETTY IMAGES/FLICKR RF)

Yes, yes, they did say that it would be hot in Florence.

But nobody said this hot.

This, I think as I navigate the 463 steps you must climb to explore the mammoth cupola crowning the city’s famous Duomo, is not just heat. This is an inferno, a body-melting ordeal: Look at the streams of sweat pouring down my face and neck. And I’m going down the stairs, not up.

It’s half-past noon, the sun is high in the Tuscan sky, and the temperature is 98 degrees — and climbing. Such has been our weather here, day in, day out. Clear heavens, broiling orb. Record-setting August temperatures — 99, 100, 101. And more.

The day we visit Siena, we’re lucky: It’s only 100 there, higher up in the hills, while Florence withers at 104 degrees. “Very unusual for us here,” says the hostess at the restaurant where we eat back in town that night. Just our luck.

Michelangelo's David, Florence. (Alla Dreyvitser TWP/twp, phto by bigstock)

And speaking of night. It’s cooler in the evenings, they say? Hah! In the apartment where we’ve been invited to stay (free digs! who could refuse?), the air’s stifling. We throw the windows and shutters open wide before bed, praying for a breath of breeze — and get whomped with mosquitoes instead. I wake in the morning with bumps on my back and my hair so wet you’d think I’d been running through a rainstorm. (I wish.)

Perhaps you wonder: Is there no air-conditioning in the apartment? Hah again. This is Italy! Where there is not very much air-conditioning at all. Yes, some restaurants are cooled — barely — and some shops, but given my husband’s anti-purchasing proclivities, we can only peruse the purses and wallets for so long. In the museums, portable air-conditioners labor to overcome the effects of hundreds of sweaty bodies passing through. Guess what? Can’t be done.

There is, in a word, no relief!

Until we come up with the five-star cocktail hour.

I don’t recall whose idea it is, if anybody’s. I think it just happens because my husband wants a drink. And because he puts on long pants.

That’s so he’ll look decent (he’s from the South) going into the bar of the small hotel next door to our apartment. We sit ourselves down in the funky oversized chairs, but the bartender’s busy on his cellphone. Outdoors. We wait. And wait. And — we start to sweat a little. Not because my husband’s anxious to order, which he always is. But because the hotel’s cooling system blows . . . uh, not exactly cold air.

“It’s too hot in here,” complains Anson, tugging at his trousers. “Let’s go someplace else.”

But where? “I think,” says my friend Judy, pondering, “that we’d have to go to a five-star hotel for really good air-conditioning.”

Of course! A luxury hotel can’t let its patrons roast! It will cool them commensurately with every penny they pay!

“Let’s go to the Hotel Savoy,” I exclaim, remembering the ritzy-looking establishment we’d admired while sitting in the piazza earlier. After all, we’re dressed up! We have credit cards! We can afford just drinks!

So off we traipse. “Buona sera, signora!” call out the desk clerks as we enter the Savoy lobby. Everybody’s so welcoming! In the elegantly plush modern bar, the waiters hop to and we’re soon basking in climatic comfort. We raise our martini glasses in a toast to our smarts, then sip the drinks verrrrry slooooowly as the sweat evaporates from our skin. The waiter brings a tray of treats — mini-crostini, olives, cheeses — for us to munch on. And a second when we finish that one. We relax. We feel very cool. In every sense. This is the life!

So. Now, during the day, we’re the dutiful tourists, trudging through the Uffizi, ogling Michelangelo’s David, ambling through the San Lorenzo market. We glug bottled water continuously, fan ourselves feverishly, wipe away the sweat that gushes from every pore. But our eyes are on the clock, counting down to martini hour. Come 5:30 or 6, we bag it all for a luxurious climate-controlled interior and super-attentive service.

Because it’s always laser-focused upon us. Getting off the bus back from Siena, perspiring and, um, well-perfumed, we head straight for the Hotel de la Ville on the tony Via Tornabuoni. The bartender seems so happy to see us! “Benvenuti!” he calls excitedly. I push the wet hair off my forehead, wondering if he’s talking to somebody else, but nope, there’s nobody else around. He fixes us some mean martinis and gestures to a large table of finger foods. “Please,” he entreats us, “have some snacks.” When we finally get up to leave, two drinks, two hours and many munchies later, he’s sorry to see us go. “If you ever want to come back,” he says plaintively, “I will be here.”

Because here’s the thing: Nobody joins us on the sofas. You’d think these places would be crawling with escapees from the swelter. But no. The teeming tourists stick it out in the sticky streets. Just outside the blissfully cool bar at the posh Hotel Lungarno, we pass a terraceful of glistening diners. What’s wrong with these people? Don’t they feel the refreshing air beckoning from the open doorway? Well, we’re no fools, anyway. We settle into the white sofas with our drinks and complimentary canapes and while away the hours before dinner staring at the lights of the Ponte Vecchio. The view’s just as pretty through the picture windows as it is from the terrace, if you ask me. Prettier, even. Much, much prettier.

At the Hotel Brunelleschi, it takes the waiter half an hour to bring our bottle of wine, but so what? Just that much more time to enjoy the crisp clime of the, yes, empty bar. And wonder about the weird people with the sweat-dampened shirts sitting on the other side of the plate-glass window. Don’t they know how hot it is out there?

Hot. Hot, hot, hot. That’s what it is, and that’s what it stays, except for our daily reprieve. Of course, the day after we leave, the weather breaks and the temps plunge into the 80s.

A couple of weeks later, we’ve forgotten our trial by fire — and five-star cocktail hour. And then the credit card bills arrive. Martinis: $25 a pop.