
When you ran it up again, did you let it get hot enough for the fans to kick in? Be a good idea to do that & see what temp it gets up to (should be @96) & then when the fans kick in, the temp should drop quite quickly back down to low/mid 80's.
If the stat hasn't been replaced in recent history, won't hurt to get a (proper) new one in, just don't go for a cheap copy.
Personally I'd move the temp sensor to the metal stub for the top hose on the drivers side, just below where the fitted gauge sensor is (mines fitted with a jubilee type clip, with some high temp silicon sheilding the sensor from any wind, not that there is much there), worth going for the mod that resensitizes the gauge too.