The fan should spin easily when engine is cold, air flow through the radiator makes the clutch react to temp.
the stock gauge is good but an aftermarket gauge with numbers is better, iirc the stock gauge only has a 150* number sweep so 25* is a lot of movement on it, not uncommon for the engine temp to rise 15-20* in traffic with the ac on. I mounted an aftermarket gauge just under the dash so I can peek at the numbers and compare that to where the stock gauge is reading, I was surprised at how far the stock needle moved with only a few degrees of engine temp changed.
I put the gauge under the dash at my left knee, they make a pillar gauge pod for aftermarket gauges but I'm cheap and had the little chrome gauge things already.