Flame's End - S1-E13
Other mistake: MacGyver and Amy get locked up in the nuclear disposal chamber with the sludge coming for them. Amy says "before it reaches this room it will get too hot for us to breathe", but just as MacGyver closes the door after managing to get it open, the sludge pours in. At this point they're breathing just fine and not sweating at all.
Answer: Perhaps s02e13, "Soft Touch." Penny Parker (player by Teri Hatcher, who would have been 22 at the time) crashes at Mac's place. She performs singing telegrams and takes Mac's Jeep to her next job, but goes to the wrong house and sees 3 men torturing someone. She drives away and the men chase her, noting the license plate of the Jeep. Penny convinces Mac to help, but she's unable to remember which house it is. Later, the men find out where Mac lives and kidnap Penny and a Serbian (a guy from the beginning of the episode), Mac follows and he reveals the bad guys' plot to kill someone at city hall involved in a drug case. The three rush over to city hall and prevent a bomb from going off and the bad guys are captured.
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