I don't think it would have much if any impact on heat dissipation in a case where both cores are on the same die. In a dual processor system with seperate chips it would conceivably keep both cores cooler than one would be doing all the work, but I think roughly the same number of calories would be transferred to the air in the case either way.
Lose performance? Not in terms of any realistic comparison. The context switches are taking place anyway, whether you have one chip or two. A system with no context switches would be faster at running a single thread than a system with context switches, but that's DOS

.