My experience is that my '76 will boil over before reaching 'H'.
I presume the car stood for a while before you inherited (sorry for your loss BTW)?
It may be worth backflushing the cooling system, however it would also be worth checking the actual temperature the car is reaching, just to make sure it's not a faulty or mismatched gauge/temp sender...
You don't say where you are located?
Oh, and welcome to the forum BTW. We like

here!

Cheers,