Totally environmentally unsound... but.
We got this roller which has sticky paper on it. One sheet does a large area it picks up lots of lint and particularly bunny fur... When it no longer picks up stuff, you tear off one sheet and the next layer is ready to go. It is useful for fur. My daughter even ran it over Binky Boy. He didn't seem remotely perturbed. Lots of loose fur came off. Bit like waxing minus the ouch factor.
He is not enjoying the heat much. We also got him an aluminium mat. It is like a metal doormat made of slats which are hollow. He just sprawls out on it on his tummy. It stays cool without any need to do anything. He doesn't chew it. Here it cost around $25 I think. It folds up too.
i used to have a roller like that, went through several rolls of sticky paper til i realized it was costing too much.. and yes i used to roll it on Binky's back too! now i use clear packaging tape for fur on clothes and hard to clean areas.. but tiny fur balls are constantly rolling around on my floor now..
that metal mat sounds like he's on a barbeque grill!