Definitely remove all oil, and heat the part, it's the step most folks miss. Heat makes "cold" blue look better, and last longer.
A heat gun is about as hot as you'd want to get it.
I just bought a new gun, Steoger Condor, and the is some rust on the barrel and reciever. I would like to try rebluing it myself and was just looking for pointers how to clean it up and what would be the best kit to use.
Thanks,
Adam
PJ's products express rust bluing.