Well, unless the thing is some sort of precious family heirloom or ultra-high-end beastie you’ve spent thousands on, my advice would be to suck it and see.
Stick it on its side and see what you think - if the CD falls out of the tray every time you try to use it, or it keeps crashing unexpectedly, then revert to an upright position.
It’s pretty unlikely that any standard component is going to explode in a ball of flames because of a change in orientation. I agree that if there is a problem it will be related to airflow and cooling, but the incremental overheating from a change in orientation is unlikely to cause any permanent damage, just instability.
I am fairly certain that the concept of heat rising has little practical effect here. First, warm air masses do rise, but only compared to cooler air masses. In a small computer case this kind of differential would be trivial. Second, the passive convection of heat is a fairly minor force compared to the powered fans that are actively moving the air through the case.
Think about it, if this were really a problem, why would they manufacture horizontal cases at all?