1) Go massively overboard with the insulation, and use nonflammable insulation.
2) Put the keg on your burner and give it some heat (stirring the whole time) without insulation.
It's the standard trade-off when maintaining temperature in any application. You either insulate (and deal with the difficulties in adding heat through/around the insulation, and difficulties with the insulation itself such as the BPA issue you mentioned), or you heat (and deal with continually adding heat, as easily-heatable containers such as kegs are not well-insulated). I'm using a cooler now, but I plan to go HERMS in the not-too-distant future, and when I do that I may get a keg for my mash tun, as I will be able to deal with the heat issues.