What I did was use the bezel of the thermometer as a frame, and inset half of the globe into the frame and made it into a clock. I also discovered a good use for the other half of the globe, which I'll get into in the last step.
Step 1: Cutting the globe & adding the clock
I drilled a hole in the end (North Pole) and mounted a quartz clock movement. I guess I could have stopped here and just mounted the globe clock on the wall, but I wanted to make use of the old thermometer housing.
Step 2: The thermometer
Step 3: Preparing the thermometer housing
Since glue was stuck everywhere (after removing the face), I decided to glue a piece of black posterboard where the face had originally been (photo 3). I figured this would be easier than trying to get all the sticky glue off.