Coolant over temperature when climbing long or steep hills?

My car was going into limp mode a few months back any time we had to drive a slight incline, or the outside temperature was hot. The dealership replaced my thermostat as they found it wasn’t opening properly.

The car drove fine for the last few months but now once again it has started to display the coolant over temperature message when climbing steep or long hills. I’m in Australia so it’s coming into winter and the outside temperatures are not very hot. After some google searching, I came across one of your videos on how to replace the fan clutch and a lot of websites said the fan clutch has probably stopped functioning properly.

The other strange thing is when I pull over in the middle of a steep hill because of the overheating, once the message goes away, I can drive up the hill from a standstill with no issues. It only seems to be a problem if I try to go up a steep hill with momentum, which I lose speed rapidly. How is it that I can’t maintain speed, but I can take off from a standstill without any issues?

My main concern after doing some research is that most people only seem to mention overheating, whereas I seem to have a lot of loss in power too. I have the accelerator pedal flat to the floor and the car still won’t rev any harder or pick up any speed. In fact, it just continues to lose speed and won’t drop a gear unless I do it manually with the automatic transmission (this usually results in the over temperature message appearing sooner). Do you have any thoughts on what the issue might be if not related to the fan or thermostat?

I should also mention I’m towing a caravan which is about 3 ton. We have been on the road for almost 12 months. There were no issues with towing up hills for at least the 1st 6 months or so. It’s been constant issues for the last few months.

Thanks!