We had this argument before over on the "We aren't rich but we aren't stupid" thread.

Although a number of variables are in play, the slight amount of extra heat in the engine bay from street/strip turbo systems  is easily managed and has no ill effects (unless your air intake is positioned over the exhaust or everything in the "bay" is made out of cheap plastic).

Millions of OEM turbo engines prove the "extra heat" isn't really a problem.

Technically, most tubular exhaust headers radiate "extra heat" into the "bay" because of their thin-wall construction and greater surface area.  But nobody's complaining about that.

In fact, generally the more power you make, the more "heat" you make. 

And belt-driven superchargers can cause crankshaft and main bearing problems (even failures), belt slippage/belt loss,  and other complications (while sapping 70 h.p. or more power to turn under "boost"*) 

And most of us have seen a N20 fireball or two . . . .

So no poweradder is without some downsides.  But all things being equal, the advantages of turbocharging far outweigh the disadvantages.

*A turbo can compress similar amounts of air at a net cost of only 20-25 h.p., primarily because most of the energy that drives a turbo would otherwise be wasted.