Welcome on here and congratulations on choosing one of the range of the best classics.
Since the car is a recent acquisition, the first thing I would ask is ...
Was it the previous owner's daily driver or was it a museum piece ?
( The point being that a museum piece will not have been run regularly and the cooling system may be coked up.).
What is the antifreeze like in the thermostat outlet when cold.
( If it is a nice translucent blue that is good. If rusty that is bad news. )
Has the previous owner used waterless coolant ?
( If so then yes, it will run hotter.)
A drain and refill of the antifreeze may be a good idea anyway. Check the drain plug on the nearside of the block. This is likely to be gunged up. No downside to this.
If you do decide to change the thermostat, ensure it is the correct one with the extending foot at the base so it closes off the bypass port when hot. And while you are at it, check the small drilling in the thermostat outlet top is clear ( it goes to the water hose at the top of the rad; and acts as an air bleed to this point. )
Some other questions.....
Does the heater work ?
Is the IGN timing O.K. ( I note you have been running at idle when there is not much advance. If it's very retarded it will run hot.)
Does the dashboard temp gauge work and what does it read at various stages ?
Does the service record indicate that the rad; has been reversed flushed through recently ?
Again, is the engine running on a very weak mixture at idle ? This will also make it run hot.
Again I've never been a fan of those I.R. temp sensing guns unless they are used with an electronic thermometer first to determine the error as the emissivity of the surface will affect the reading.
I think the first thing would be to verify the water is actually running hot with an electronic thermometer and use the in dash temp; gauge for subsequent measurements.
Lots of questions I'm afraid.
Good luck with it,
Tony.