It's a more common 'problem' than you might think. Reason is, the standard Ford temperature gauge sender is not right for the Morgan instruments of this age. So a replacement sender could easily be the wrong one.
That means the earlier advice to check the running temperature with a thermometer is totally the right first step. Any good real garage should have one - if they haven't, go elsewhere
At the manageable risk of burning yourself, you could try this. Start car from cold. Feel the top hose, it should be cold, but there is a small 'leak' in the correct thermostat so it will warm a bit. But the hose will suddenly get very hot, when the thermostat opens. Remove hand to avoid burning (as if I needed to say) and leap round to the dash and see what the temperature gauge says. Should indicate roughly 'N' for normal, but if the gauge says anything much above N, then I suspect a gauge/sender problem - not an over hot engine.
Do be aware though, the radiator could be blocked and not working properly, it's not unknown either.
I don't know what the correct sender is, my 4/4 has the wrong one, but I've modified the gauge to read correctly with the Ford part. Seemed easier to me!