I suggest letting the engine idle long enough to put the cooling fan on, then note where the gauge reading is, and how hot the heater is, if it is a lot hotter than normal, it does point to a stat, in which case the gauge should also be showing warmer, remember though 4-6 C will produce a noticeable difference on the gauge.
The way these gauges work, they are not terribly accurate at either ends of the scale.
Stat and sender easy to do though.
tabetha