It could just be the temp sensor / gauge. It's certainly not unknown for the 20v gauges to read between 70 and 90 (usually about 75 like mine is) on the gauge but to quite happily be reporting around 88-90 when plugged in to diagnostics. So there's every chance your 16v could be the same given it's at least the same stat if not everything else (is it the same gauge on the GT? dunno!)
If I plug mine in to Fiat ECU scan it shows around 88. Also on Torque (Android app) it declares around 88. Gauge never exceeds around the 75 mark! It's on the third thermostat since new though and the previous two were definitely shot when I changed them.
Before a remap you need to make sure everything else is "correct" - clean and working EGR valve, clean air filter, fuel filter not overdue a change, clean MAP sensor etc. In fact making sure all your "bits" are sorted may just do the trick in the first place!
Check out the brakes as well incidentally - pads sticking is not uncommon in my own experience, and others AFAIK!
Half a tank on my 20v is usually worth around 350 miles I think. Mines a 63L tank but dunno if the GT is?