Well, eating would mean you're not doing the MC, since the whole point of fasting is to induce a state of cleansing, which is only done when the body isn't digesting solid food.
However, I think that experiencing very hot temperatures while on the Master-Cleanse could actually be beneficial, because sweating would help you to rid yourself of some extra wastes. Just make sure you drink a lot of water, and you'll be alright for sure!
The only downside is that your sweat might smell like cayenne pepper! (at least mine did).