When I replaced the radiator on my 94 F150, the transmission cooler lines wouldn't stop sleeping until I put a little of the liquid Teflon on the threads. Been good for the last 3-4 years now.
Pieces of the Teflon tape could get lose and cause issues, but the liquid stuff seems to be better. Just a small dab, and the act of threading it in distributes it well. The fittings on the replacement radiator might not be an exact match to the fittings on the lines.