If you are quite sure that the thermostat is installed properly, then it is possible that the new thermostat is not opening at the correct temperature.
You can avoid the "mess" just my putting a pan under the radiator and pulling the lower hose. Then, you can take the thermostat out and test it in a pan of water to see when it opens fully.

I do have a question/suggestion:

Prior to doing the above:

When the temperature climbed to 100 degrees, was the radiator cap on or off the vehicle? If it was on the vehicle, you may wish to leave it off the vehicle and try the process again. Any air in the system is now permitted to exit via the radiator cap at the tank. You may see the coolant level in the tank drop significantly and you can add more coolant while this is happening.
It might be worth a shot prior to removing the thermostat. Remember, bad thermostats are not all that common.