I don't think any of my cases have a cover on them. They just get in the way. Upon noticing the absurdity, I stacked up all my loose case covers and stuck them in storage somewhere.
If I'm just building a PC for myself, then I usually just prop up an 80mm or larger fan next to the cards I'm worried about (if any). I would do this with valuable cards like ISA Sound Blasters, but try to do it in such a way that you aren't adding vibration to the components in the system. A little airflow does a lot - for most things that don't dissipate a lot of heat you don't need a powerful fan, just moving the air makes a big difference from no fan at all.
With video cards, often you can improve the cooling on the card itself using aftermarket coolers or rigging a fan on them (popular idea with Voodoo3s).
With more modern video cards and motherboards that support variable speed fans, you can use tools like Speedfan to override the fan behavior to your preference. I think manufacturers tend to hold back their fans until temperatures have gotten too high, so I like to change this.
On my modern PC, I use a GTX285 which runs hotter than I'd like, especially in the summer.
I found a powerful 120mm Nidec fan at a Goodwill which calls for 24V, but will still spin with 12V. It's metal and heavy enough to stand up by itself.
For flexibility I soldered a TX3 connector on it, but then made an adapter to go from that to a barrel connector. I use a 24V wall wart to power it at full speed. It's loud so I just plug it in when in a game. Not very "professional" but it works. I have the fan sitting on an old box of checks (remember those?) just outside the case, so nothing in the case picks up vibration from it.
It would help more if the GTX285 had an exposed heatsink, but all air has to go through the card's own fan. Still, blowing wind across the card's intake fan keeps it's air at room temperature, which has lowered the GPU temp by 5C.