accord 90-93 air con fan running non stop

Odd problem - air con fan runs intermitantly.
Works ok when I turn on air con - then goes off when I switch it off.
Engine fan ok. Air con fan seems to keep coming on - so engine is running t
oo cool. Temp guage dropping to real low when cruising in cold weather.
I noticed it recently - I had a bad key stuck in the lock at 1 position. So used spare key to lock door and left ignition on aux. Thats when I heard t he air con fan - like three hours after I turned off the car - still runnin g ! Had to split the ait con fan connector or the battery would have been t oast.
Could this be a faulty ect B plug ? like - telling the system its over temp when its not ? Thats an easy one to check.
Geoff - Bristol. UK.
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