Why doesn't this cause heat damage? The reasons are simple:
1. Heat is not direct
The heat is not applied directly to the hair, it's over a shower cap so it is much less intense.
2. The conditioner creates a protective seal
At the time you apply heat, your hair is covered in the conditioner and that in itself acts as a strong heat protectant.
3. Water's "specific heat" temperature is very high
The specific heat is the amount of heat required to raise the temperature of a given quantity of 'something' by one degree Celsius. A lot of energy is need to increase the temperate of water by one degree. Conditioner's key ingredient is water.
Water acts as a buffer between the heat and your hair and slows down the rate at which your hair fibres take in the heat.
It also follows that if your hair is very well moisturised, sealed (e.g. with coconut oil or an oil blend) and has been recently deep conditioned, styling tools that use heat are much less likely to cause heat damage.
Ref: The Science of Black Hair, pages 171-2