I think that you shouldn't put paper, carton or anything easily inflammable near your rig, don't think?
lots of guys build rigs on top of old motherboard boxes, plywood, and other materials, this is no different. I've seen really nice rigs made entirely from wood. And no, i don't think it's that dangerous. Everything is fuse and breaker protected, and we build with flammable materials in our homes and offices all the time.
It would have to heat up to 200-300-400c before it caught fire. Even if the cooling failed the computer would crash/shut off long before that. The fan would melt off long before that.
Black asphalt in the summer is probably hotter and I'm not aware of cardboard bursting into flames.