I feel like everyone always tried to fix a cooling problem with some "better" part, but it seems they really just don't know how, or don't care to spend the money to replace or fix the underlying problem. If you're system is working properly, like Tim said, it should run perfectly and within temps under all (normal) conditions. Of course this doesn't include jeepspeed blasting through sand, towing through the sierra's, etc. Start with a decent radiator. Get a new water pump, get the correct thermostat, make sure your e-fan is working, no clogs, correct coolant level and mixture, working rad cap, and you should be golden.
My last jeep had the cleanest, and best working cooling system I've ever experienced. Never once did it go above 220, and all parts worked immaculately the entire life of the vehicle.
My current jeep has the WORST cooling system I've experienced. Mud-sludge coolant, clogged passages, non-working e-fan, clogged heater core. And of course, it heats up real quick. I have come to grips with the fact that to rid the problem, EVERY bit of the engine that sees and touches coolant must be replaced...
Now we're back to the original post. Why are you putting in a 180 degree thermostat? There's really no need.