I have a 2001 F250 Super Duty. The heater keeps running even when the truck is turned off. Have a dead battery every morning. What is the cause?

I suppose it might be a sticking relay or a bad ignition switch.

Your saying the blower motor runs, even with key off and out? Do you turn off the hvac controls? If it you do, does it kill the blower motor? Note the diagram, if you pull that 40 amp fuse, it should kill the blower motor. Or pull the blower relay, that should kill it till you figure out the problem. See the 10 amp fuse, goes hot with key on, you can use test light to check for voltage. That fuse shouldn't be hot with key off. If it is hot, I'd have to check ignition switch. The relay has a load side and control side, the control side needs voltage and ground or the relay won't energized.