High idle temp with radeon 3450 (passive)

There's not much you can do with the slim cases since they are just cramped for space with limited air flow, but that seems too high for such a low-end video card.  Did the card come with your computer or did you buy it on your own?   How long have you had this card and did it always have these high temps or just recently?  Is there any dust build up on the heatsink?   You may want to look into one with a fan or a better heatsink if it continues.  However, 75C may not be out of line for a passively cooled card.  I think 64C at idle is too high for this card though.  It probably should be around 50C, but you will probably have higher temps in the smaller cases.  A lot of members have or had the 3450 in the slim cases so maybe they can offer their experiences. 

I put the card (ASUS) in right when I got the computer 2 weeks ago. Could I just take off one of the plates covering an expansion slot next to the card? I was also thinking about getting an expansionn slot exhaust fan but don't know how well it would work.

You will just draw more dust in by removing a plate cover.  As far as PCI slot fans go, some seem to think they work and others say they do no good at all.  Asus makes quite a lot of the HD 3450's.  I'm not sure which one you got, but you may want to contact their tech support regarding the high temperatures.