To diagnose this the fan relay is the pla...

To diagnose this the fan relay is the place to test. The relay is conceptually two circuits. One high current circuit and one low current circuit. The concept is that the temperature sensor tells the computer that the temperature requires the cooling fan to come on. The computer then either grounds the low current circuit or feeds it with voltage. This closed circuit then completes the high current side of the relay, which runs the fan. So your fan continues to run for one of two reasons.
1. If you find that the low current circuit is open (meaning no current flow), yet the high current side is still closed, then you have a bad relay.
2. If you find that the low current circuit is closed, it is because the temperature sensor is bad, causing it to tell the computer the engine needs cooling after the temp drops below the range when cooling is needed...Is this expensive to get repaired? I tried looking up cooloing fan relay at Advance Auto got no results does it go by another name?