Could I have a bad thermostat? Most likely. specially if the rise in temp is when you are going uphill. You can actually take out the thermostat and test it before replacing it with a new one.
Do I have to get the thermostat from the dealer or is there a cheaper alternative? I would get it from the dealer. It is not expensive. You can order on-line, but make sure it is for your model/year MB. good on-line source that I always order parts: www.importec.com
How hard is it to change the thermostat on my car? It is probably one of the easiest tasks.