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The oil temperature sensor is in the area above the oil filter. You can get under the car and check it's connections and make sure it hasn't say loosened up or carry damaged wiring.
If memory serves me correct it's position relative to sitting oil is right above the full point with the correct amount of oil in the car. That being said it may be best to service it when you're going to do an oil change as you would have to get under car, remove filter and drain oil anyways.
Mine started reading weird in the cold weather too.
I just got it replaced last week.. Not hard.. Just remove oil filter.. Unplug sensor,
unscrew with a 19mm wrench.. I went back to the AC delco unit.. Seems to be ok
now, but havent' driven it yet