Fans should not be on while moving, the purpose they serve is to cool when there is insufficient natural air flow which happens when at a standstill. Standard fan switch is fine on standard rad but it can suffer Heatsink effect with alloy rads as such as said MSD sell an "Uprated" one it's actually from another car, this closes at 92C hence fans on and off at 88C so few degrees span, where as the standard closes at 86C and opens at 77C and so the reason why the fans stay on for while!

As said thermostat will do nothing. I once had a problem with mine could not work it out fans stayed on all the time and was running hot, eventually figured it was my tired engine burning so much lubricant was the reason for hot running but probably not your problem.

The fact it runs hotter than usual shows the fans to be doing there job so new switch won't solve anything they rarely give trouble anyway more the OEM loom does.

I would check to make sure coolant circulation is ok.

Martin