90 miata battery overheating

90 miata been sitting 4 years. We got her up and running but still having some problems.
We tried charging the old battery (build date 6/18) it took a charge and AZ says tested ok
My problem is after driving the car five minutes the battery is hot (170f).
I thought maybe over charging so I pulled out the good olvolt meter and this is what I know.
Not started- 12.09v (yes not standard 12.6v so it's a little low)
Running 800rpm no real load-12.8-12.9v
Running headlights on-13.2-13.5v (1200rpm- 13.6v)
Over all it seems to charge fine. So what else is making my battery hot? I've never messed with these AGM batteries

Well I replaced the battery. All seems to be going well.