The area needs to be thoroughly cleaned and dried or the heating can bond some of the muck to the paint.
Warm GENTLY with Hair Dryer. (Ask the other half nicely to borrow it) Or you can use hot (NOT BOILING) water poured on slowly over a period of about 30s - 60s.
DO NOT OVERHEAT OR PAINT DAMAGE CAN OCCUR
You want to heat up the badge enough for it to start moving a bit when you push on it.
Use dental floss to cut the adhesive. Wrap the ends around your index fingers or two small pieces of wood.
You will need to create a sawing action my moving your hands back and forth to pull the floss through the adhesive.
There should only be a bit of adhesive residue left on the vehicle, but the badge itself should come off in one piece.
If it cools off before you finish give it a second warm.
You can remove any large pieces of residue by using your finger nails or an old credit card on them and then applying some WD40 and elbow grease.
Finally remove any shadow by using some mild cutting paste and polish.
You will most likely be able to remove the entire badge without breaking it using this method.
The only drawback is that in some light conditions you may still get some shadow effect where the badge was.