What is the medical reason behind avoiding hot foods and drinks post op?

After having surgeries of the face such as rhinoplasty, face
lift, chin augmentation, it is best to avoid hot food and drink. This is
because heat vasodialates, and cold constricts. Vasodialation (widening
of the blood vessels) can cause bleeding and excess swelling. It is best
to refrain from eating or drinking anything of a hot temperature until
otherwise directed by your surgeon.

Different surgeons may have different instructions to follow after rhinoplasty.  If you are instructed to avoid hot food and drinks afterwards, it is because hot food and drinks could potentially cause bleeding from the nose after surgery.  Hot food and drinks can cause the blood vessels to dilate, and this in turn can lead to bleeding after surgery.  

Avoiding hot foods and drinks after rhinoplasty is a good idea as the nerves that supply sensation to the roof of the mouth and front teeth runs in the floor of the nose and can be affected by septorhinoplasty.  Occasionally patients will have numbness post op which is usually temporary and the possibility of burning the mouth is a possibility if you were to drink or eat hot things.