The temperature was running high, and so were the tempers, as top-seeded Jimmy Connors defeated Chilean Davis Cupper Hans Gildemeistar, 7-5, 6-4, to advance to the semifinals of the $175,000 Washington Star International tennis championships yesterday.

A thermometer on the center court at the Washington Tennis Stadium registered 107 degrees, and for a few minutes the scowls, heated words and defiant gestures Gildemeister and Connors directed at each other made it seem even hotter.

They were locked in a grueling, hard-fought match, and at one stage it threatened to explode like the radiator of an overheated old jalopy.

A bad line call against Gildemeister on a critical point - at 5-5, break point against him - precipitated the unpleasantries.

Guildemeister argued for nearly five minutes with first the line umpire who made the call and then the chair umpire, who chose not to overrule it.

Finally Connors and Gildemeister exchanged words behind the umpire's chair, and later mocking gestures, as the match took on acrimonious overtones.

The crowd rallied behind Gildemeister, the underdog who had been alighted, but Connors always works well in an atmosphere of villainy.

He was more determined than ever to win, held serve after two break points and four deuces to win the set, and then sprinted to a 3-0 lead in the second set before Gildemeister broke back to 2-3 and pushed him the rest of the way.

"It was hotter for him because he was the one out of control. I kept control pretty good and concentrated well, Connors said. "I tried not to let anything bother me. I just kept playing."

In today's semifinals, Connors will play Jose Higueras, who was too patient and ultimately too aggressive for No. 6 seed Harold Solomon. The 25-year-old Spaniard stayed with Solomon through long, tedious rallies until he got short balls on which to come in and won a terribly boring match, 5-4, 6-4.

Higueras led, 5-1, in both sets, let Solomon back into them, but then choked off the Silver Spring native's comeback attempts.

Higueras has beaten Solomon the last three times they have played, all on clay courts, and each time he has done it pretty much the way he did yesterday: trading top-spin loopers and "moon balls" until he got one short enough to dash in and volley, or to thump with a forcing ground stroke.

Higueras, winner of two small Colgate Grand Prix tournaments (Nice and Cairo) this year and a semifinalist in the U.S. Indoors and Italian Open, also made judicial use of the drop shot off his backhand, drawing Solomon to the net and passing him.

"His game is a replica of what mine used to be. Right now he has more patience than I do," said Solomon. "He kept the ball pretty deep and attacked better than I did. He's stronger than I am and serves better."

The Solomon-Higueras match was something of a sedative. The Connors-Gildemeister opener was both better tennis and better theater.

It provided an interesting contrast in styles - Connors trying to bore in, slugging his left-handed grounds strokes flat and deep, Gildemeister roaming the backcourt with his unorthodox style - standing upright and cranking deceptive top-spin ground strokes, two-fisted on both the forehand and backhand.

Gildemesiter was serving well (five aces) and thrashing some high-velocity winners to match those streaming off Connors' steel racket. He broke for a 4-2 lead in the first set, but immediately lost his serve, dropping seven consecutive points from 4-2, 30-0.

They stayed on serve until 5-5. Gildemeister double-faulted to 15-40, saved on break point with an ace and another with a forehand cross-court blast that seemed shot from a cannon.

Connors got another break point when Gildemeister hit a groping lob long off a forcing forehand. This was a shot Connors capitalized on throughout the match, charging in to take a short, high ball on the rise and drill it deep.

It was the next point that added hostility to the hostilities. During a rally, baseline umpire Norman Fitz of Silver Spring called good a Connors shot that was clearly over the baseline.

Connors won the point with a high forehand cross-court put-away of another highbouncer, for the crucial service break, and Gildemeister was furious. He circled the area beyond the line where Connors' shot had landed. The crowd knew that Fitz had blown the call, and they supported Gildemeister as he argued passionately.

Finally, after several minutes, net judge Jack Tiedemann of Washington ran over and directed the red-faced and agitated Gildemeister to stop arguing with Fitz and take up his case with chair umpire Stewart Saphier of Silver Spring. This he did, to no avail.

At the changeover, Gildemeister thought Connors made a derogator remark to him - Connors later denied this - and the players began jawing at each other. Gildemeister wagged his finger at Connors, mimicking one of the brash left-hander's favored gestures. Early in the next game, after winning a point, he also mimicked Connors' famous hip wiggle. Connors fumed, and wiggled back a couple of points later.