you can of course fit it with heatsinks, but it's not necessary. It is normal for the 6581 to get warm/hot, but it is also in their nature to run at such temperatures. if i read it correctly, then there are only 8580 in use and there also a fan installed. I've never had to worry about anything like that (fan/cooler), nor have I ever had any problems during operation. they break when handled incorrectly (ESD).
Note the fact that a heatsink, fan or whatever you use is fine, but that is never installed inside an original c64.
... and yes, your device does look cool.