Why does cooling fan stay on ?

unlikely the fan is faulty - there is no current feed at fan until temp sensor tells it the engine is hot so fan should not operate in cool condition if sensor is ok ---usual cause is temperature sensor - if you have basic skill remove sensor and test with continuity tester etc in a container of boiling water - switch should open ( complete circuit before 90 c )and close ( break circuit ) below about 80c
While you wait to change sensor wire fan through an on / off switch and manually switch on if temp gets high -

pc6493
March 2010