Here is a DIY video on how to remove a thermostat for a 2011 Challenger R/T with a 5.7 engine. It is an easy install. First, make sure you purchase more coolant (correct type), a drop pan to catch the run-off and kitty litter (optional) to soak up the coolant that you don't catch in the drop pan. Next, trace your top radiator hose to the engine block, remove the hose and unscrew the two bolts on the neck. (Note: Make sure your engine is cool before starting this process). Take the neck off and you should see the top of the thermostat, pull it out, make sure you have the gasket that is around the old thermostat and then place your new 180 degree thermostat in the vacant hole. (Note- The new thermostat should cost about $16). Bolt up and put the hose back-on and fill the coolant reservoir up to the "full" level. Clean up any mess. Automotive Cooling Systems | Dodge Challenger Forum
I run a 180 Thermostat with my supercharger. Very easy to change on the SXT Plus. Car stays around 194 degrees instead of around 204.
With such a small amount of coolant escaping I think I would just wrap rags around the stat to catch the coolant rather than have it drip all over the engine and floor.