Brass and copper rivits don't need heating, neither do iron/steel at these sizes. To form the head you need a "Snap" which is like a nail punch but has a half round recess to form the head, infact you will need two as the factory head has to sit in one and teh other forms the head.
One problem you will get with timber below the brass is that you ar elikely to compress the wood and get a dent around the rivit if trying to form a full head on teh back. Depending on how decorative the banding/rivits are you could either just snip off the rivit that is proud of teh washer which will deform it slightly so it won't come out or just lightly pein it again to just swell it enough to hold. This is how the copper boat rivits & washers are set.
If it really is just for looks then drill the wood and epoxy the rivits in place, bit like this
