I have seen people build temporary walls in front of garage doors that worked their way around the tracks for the garage door. I saw one case where a guy did this and heated a large two car garage with two, 1500 watt oil-filled, radiator style heaters - in South Dakota no less!
But this may not be a good idea since this is a lease arrangement, although I'm also sure it could be done without affecting anything.
What I would do is cover the garage door and the surrounding area with Reflectix insulation. Just attach it with a few staples and tape the seams with foil-tape rated for this use.
To give you an idea of how effective this is, I covered the walls and ceiling of a 7' x 7' x 8' garage room that I needed to use temporarily for snakes. The room was not insulated and two the walls were exterior. The other two walls faced the garage interior, which was not heated. This was in South Dakota during the winter, no less.
The door to the room was hollow-core and was only covered with Reflectix. The gap under the door had a piece of pink insulation stuffed underneath. There were gaps in the door. Big enough that I could see light through. I left these gaps for a minor bit of ventilation.
The floor was not insulated and this is a major source of heat loss.
Here is a picture of that room before the ceiling was insulated.

I ended up heating this room with an oil-filled, radiator style heat set on it's lowest setting. I ran it though a thermostat and it did not have to run all of the time to keep the room at 80*, even when it was cold enough that there was ice on the floor in the rest of the garage.
This Reflectix really works, but you'll need to use a radiant heat source rather than a forced air heat source.