Powering off vs leaving on

If you do switch on and off many times a day you ARE better off leaving them on.
The heating/cooling cycles DO reduce the life expectancy of electronic components.
If you need to.. turn off only the amp.
The small CD and preamp electrical use are very small at idle, so leaving them on is rather easy.
I always leave the sources and pre on at all times, and my "space-heater" amp on all the time only in the winter.
If you plan on keeping your stuff a long time, leave them on.

Do a thread search on this subect in the archives, it's been discussed at great length many times.

If you amp can't run at idle without overheating, consider a different amp! There are many well made amps on the market. If you worried about Air conditioning bills, that's another thing and a valid concern.

You do not mention whether this is tube or solidstate gear.