PA 38 POH states "Warm the engine at 800 to 1200 RPM for not more than 2 minutes in warm weather and four minutes in cold.....Take off may be made as soon as the ground check is completed and the engine warm."
I believe the intent of this POH advice is to avoid spark plug fouling, a particular issue with this engine, due to excessive operation at low engine speeds where the engine can't scavenge the lead in the fuel.
My experience is that for the first flight of the day (ie cold oil) you probably won't see any movement on the oil temp without exceeding the recommended time limits in the POH. I find you generally start to see oil temp starting rise off the peg during the run up.
As an aside airplane owners should be aware that low oil temps in flight can be as damaging as high temps. In flight oil temp should stabilize around the 180 deg F mark in flight (this is the value for the unmarked white line in the middle of the green arc in Cessna oil temp gauges). Excessively low oil temp will cause higher than normal oil pressures as well as fail to ensure that the corrosive water vapor trapped inside the engine doesn't get boiled off.