I have a heat pump & its turned off but the fan is still blowing, what's up with that? The air is outside temp

Fan relay could be stuck, fan on switch might be turn on the t-stat, or stat may be going bad

Sounds like the blower in your furnace/air handler is not stopping
1st ,the question that many hate to suggest make sure the tstat is set on auto and not on fan
Then tell us what kind of furnace /airhandler you have,, elect./ gas/oil, the model number and brand