My bike completely cut out on me last night while I was going about 80KM/hr. I pulled over and lifted the seat to find a very hot battery. I suspect the regulator cooked it but how do I know? What do I look at or test to be sure. Please be gentle, I'm new to bikes and not too mechanically inclined

If it matters, it's an '89 with 13,000 kms. The current battery was installed in the spring of '09 when it had 4000 kms onit.