The heating element should not get power unless the motor is running. If it does, that typically means the element is broken and touching the frame (shorted to ground). Repair is replacement of the element.

Best not to order parts until the problem is fully diagnosed. There's a thermal fuse on the heater box that may also be blown (if the element is hot with no airflow over it). The fuse being blown won't stop the element from heating if it's shorted but the new element won't heat if the fuse is blown.

Element is part number 279838 ($45-ish depending on the source).
Thermal fuse kit 279816 which includes the high-limit thermostat on the heater box, they should be replaced together ($30-ish).

Thank you dadoes,

I've passed this information on to my husband. I know it will be really helpful!