Gym air conditioning gets blamed for cancelling a workout, and hot rooms get sold as calorie burners. Measured, the room changes almost nothing about what the session costs.
Sixteen experienced yoga practitioners ran the same one-hour class twice, in a 40 °C room and at 23 °C, with their oxygen use measured throughout. 1 The hot hour came to 156 calories; the cool hour came to 151. Heat did change the fuel mix, raising fat oxidation and lowering carbohydrate oxidation, and the total energy the hour cost stayed where it was. Heart rate did not differ either.
At rest, where a temperature effect is easiest to see, the same picture holds. Thirty-two adults spent half an hour in a room held at 18, 22, 28 or 38 °C while their resting energy expenditure was measured breath by breath. 2 Moving from 18 °C to 28 °C shifted a whole day's metabolism by about 96 calories. The 38 °C room was not statistically different from the thermoneutral 28 °C room.
The numbers sold alongside hot studios sit in another order of magnitude. Bikram yoga is advertised at up to 1,000 calories a session; a standardized 90-minute class measured 286 calories on average, with every posture rated light-to-moderate intensity. 3 Heat also takes something out of a session: skin blood flow rises to dump heat, and it competes with the muscle doing the work, so performance drops. 4
The swap is to log the work. Load and reps on the main lift, minutes at a pace, distance covered. Keep the room cool enough to do more of it, and let the number you wrote down judge the session.