You are right, the radiator is getting warm, and it shouldn't when the engine is not reaching the 84˚c marked on the thermostat.
Today, I cleaned the engine and went for a blast in the countryside in sports mode to dry it out. The gauge never went past 60˚C and was happier at just 50˚C.
When I got home and opened the bonnet it was barely lukewarm, not the usually heat radiation you feel on your face from healthy cars and some parts such as injector pipes were stone cold. I used an infrared thermometer to check various parts of the engine, the hottest were about 57˚C apart from the EGR pipe and turbocharger shield which aren't cooled. If it was the water pump, it would definitely overheat and I think would show a high temp on the gauge as the coolant temp sender is in a place where this would be detected.
The engine looked very clean, finished a few bits off with brake cleaner and used some Tectane engine lacquer. Looks like new now.
I think I'll buy another thermostat, it's a simple 15 minute job the second time round.
I'll return the old one if it makes a difference. I know I could test this one in a bucket of scalding water, but with the slight hassle of removing it, I'd rather just put a new one on while it's off as it was quite cheap from TPS.