Biologically it is always better to be cold, because you'll survive more often than not in colder environments. Our bodies evolved to deal with them because higher sources of external heat are rarer on Earth naturally.
Yes, we have sweat to cool off, but that has the caveat of being linked to blood volume. Without water you'll die, but in the same degree of coldness your body will burn brown fat to keep homeostasis, and even then you won't die until your temp drops significantly. You'll definitely die of dehydration before the high temp can denature your proteins and kill you that way.