As someone who uses a plastic mattress cover I can answer your question: yes, if you let dust build up, mites can and do start to live on the fitted sheet that you put around the mattress cover. However, it is of course easier to wash just the fitted sheet than to remove dust from within a mattress, so I think that a cover is still beneficial.

I'm not sure what you mean by trapping heat - once there are two normal cotton fitted sheets around it, I don't feel the plastic mattress cover at all.