Bad thermistor in 06 450 sprtman?

My symptoms are that on my 06 sportsman 450 when it's completely cold that the fan runs anytime the key is turned and has drained the battery (possibly indicating it's running when the key is not on?) When it is started, it immediately has the HOT indicator (and blinking speedometer hand) comes on. This is when it is cold remember. My ohmmeter died so I haven't tested the resistance, but from what I can tell in troubleshooting it, it has to be a bad thermistor. Is this right? I went ahead and started it and it sounds fine/works fine as far as i can see.
If not, what else do I need to check?
Thanks in advance for any insights.
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