Temperature plays a very important part when you are making soap as it can effect everything about it throughout the process i.e. aroma, colour and the final product.
Once you have finished pouring your soap mixture I suggest you cover it with a blanket or towel to keep it insulated as it goes through all the stages and starts to cool itself down. This will ensure that the temperature does not start to fall and interupt the fianl heating up stage and it will also prevent any flying insects or spiders dropping into the mixture at this stage.
Another very important reason for insulating your soap is to promote the gel phase. This is part of the saponification process where the soaps starts to heat up and become very warm - around 180f. You can see in the photo below that the appearance start changing in the middle and gradually works it way through the whole soap before everything starts to cool down again. Allowing your soap to go through this stage ensures that colours remain vibrant and helps you unmould the soap when ready.