Agree with newbee. Leave it powered up, and your DAC as well. Also, play any kind of CD on repeat, constantly. That way the source components will always be ready for your listening. The CD mechanism, like any revolving technology will wear out less if it is running constantly and the bearings are running at their designed operating speed and temperature, compared with start-stop operation of 0-500rpm time after time, when cold.
However, all of the above said, you still have to get your amps, analogue cables and speakers warmed up to hear the best out of them. If you have room temperature control, experiment with that too. I find the optimum (and still comfortable) room temp to be a constant 72-75 degrees F / 22-24C because this stabilises the air density and improves the air coupled performance of my speakers.
I WOULD NOT put my CD transport anywhere near a power amp. This is likely to degrade the sound due to EM & RFinterference.