As longs as there is a good way for some air to escape (vents) you should be fine. That's assuming your PC has its normal fans attached. CRTs tend to run a bit warmer than an LCD but most games back in the day didn't have or need active cooling.
Thanks @meyer980
That's what I figured when I originally built it in 2010.
This used to be a large monitor pointing up to a mirror.
Thing is, the best place to put a fan would be somewhat where the monitor is, so prone to be visible trough the front glass.
The PC has 3 (somewhat noisy) fans - front intake, rear exhaust, CPU fan.
No cover. There's 2/3 of the cabinet for heat to accumulate.
The cabinet has a few opening on the lower back for cool air to come from, and transport handle holes on the rear top, for heat to get out.
I may put one small exhaust fan & grill up top to run everything cooler...