Is placing a computer in a desk hold a bad idea?

I'm considering buying a new computer case but it's actually too big to sit on top of my desk like my current one. There is a square hold towards the bottom of the desk that would accommodate it's size with about an inch or two of surrounding space to spare. The case will have 5 or 6 fans and the desk its self sits on carpet. I'm worried that the computer will just get filled with dust and get too hot because of it being so close to the floor and in a confined space. The computer is a medium range gaming pc and the reason I'm buying a new case is because the new GPU I'm buying (which has 3 fans its self and vapor cooling) doesn't fit in my current case. I can't think of any other way around this. Will this create a big problem?