2002 wont crank when hot

[BigRed77]

Geez this is frustrating

So today I stopped by a golf cart shop while I was in the big city (an hour away)
I picked up a White-Rodgers solenoid like the one linked by CP241 above, while there the guy an obvious old mechanic type, suggested checking wire connections, since a loose one could me made looser by the heat of the engine

Well I'll be damned, I get home and fine a loose wire blade plug that comes from one of the small lugs on the solenoid
Fix it and cart runs great, all over the hood, for over an hour start and stop many times over

Then, grandson wants to ride his little tractor on the road. So we go cruising
Obviously low speed start and stop for the golf cart to 'keep up'
After about 15 minutes of this suddenly, my golf cart doesn't want to go.
Different this time than before though
This time its actually cranks, but just barely, like the battery is dead

Again though, we wait around for it to cool down a bit and it cranks just fine

Get home and the voltage on the battery is low
Like 8. Something

Wait around for it to cool off and the batter voltage is back up to like 11.8

I had just bought a new batter for it about a month ago, and I thought it had given out when I first had a problem, hut i took it in and they tested it and said it was fine