heat

Make sure you do not run them with the cover on or you could hurt something in the long run but you can cover them any other time you want to.

Second the air purifier. 

Don't cover when in use. +3 for air purifier, I don't run it while listening. I just installed one for the entire house.

I run ’puter fans for heat removal, and anything vented has a shelf above it. Prefer practical over pretty.....although can be made so if desired.

I have to be next to them to hear them...

Agree with @oldhvymec's recommendation of silk. I keep my tube integrated covered with a vintage scarf I found among the things in my father's house. It takes seconds to put on or take off, can't create any wear on the amp finish and looks far better than any equipment cover I've seen. There are more than 26,000 vintage silk scarfs listed on ebay, most for less than $20.