Three tips I learned about carmelizing onions from TV shows, and I have tried them all and they work:
1. Add a bit of water at the start. The steam will warm the onions through and get their moisture released more quickly.
2. Salt will also help draw out the moisture. Moisture prevents carmelization, since evaporation cools the onions to a point below the temp where carmelization starts (around 350 degrees F).
3. Add a sprinkle of sugar to the onions once they have reduced in size (which means the moisture is gone and the internal temperature is rising). The sugar will start to carmelize, and this somehow gets the carmelization started more quickly in the onions. I don't really know how, I only know it does seem to the speed things up a bit.
The big thing is patience. You can start at medium while cooking the onions down, but then the temp has to go down. And stir every now and then.
If you carmelize onions with a bit of star anise, and add them to any meat dish, you will get an amazing flavor enhancement of the meat. I learned that one from Heston Blumenthal.