The heat gain in your room will be affected by the amplifier since nearly 100% of power consumed by the speaker is converted to heat.
If you have two amplifiers, one being a 100 wpc Class A and the other a 100 wpc Class AB, both will pass through the same power to the same speakers. However, the Class A amplifier will consume about 1,000 watts of power at idle and at rated power and that will be converted into heat as long as the power is on. The Class AB amplifier will consume about 175 watts at idle and 400 watts at rated power. The heat transferred to your room will vary from 175 watts to 400 watts. Therefore the room heat gain will be a lot lower with the AB amplifier since the heat gain from the speakers will be the same with both amps (listening SPL and duration being equal).
If you have two amplifiers, one being a 100 wpc Class A and the other a 100 wpc Class AB, both will pass through the same power to the same speakers. However, the Class A amplifier will consume about 1,000 watts of power at idle and at rated power and that will be converted into heat as long as the power is on. The Class AB amplifier will consume about 175 watts at idle and 400 watts at rated power. The heat transferred to your room will vary from 175 watts to 400 watts. Therefore the room heat gain will be a lot lower with the AB amplifier since the heat gain from the speakers will be the same with both amps (listening SPL and duration being equal).