It could be overkill but then I'm not sure I understand exactly what's going with the heat tape, etc. Let me outline what the JM's need in the way of winter protection and then you can decide if your set up works well or not :-))

It is extremely important that once the trees enter dormancy, they remain in dormancy. That means you should be shooting for temps that don't exceed 45F or drop lower than about 25F. Consistency is important! You want to avoid situations where the greenhouse/cold frame heats up during the day or gets excessively cold at night.

Light is not important during dormancy and the containers only need enough moisture to prevent from drying out completely. IOW, an unheated but attached garage may offer better winter dormancy conditions than the cold frame.

I am not familiar with Utah winters so not sure how bad it can get. The top growth of a containerized Japanese maple can easily tolerate temperatures well below freezing - to minus 10-15F. It is the root system that is most vulnerable to cold damage and that can happen with containerized maples at temps below 25F for an extended period (2-3 days or more). So the ideal situation for winter protection would be somewhere where the planted container remains below 45F but above 25F. In many colder climates, that is accomplished by storing in the garage or heeling the pots in to the soil or mulching around them with a thick layer (4-6 inches) of straw or mulch. Bubble wrap works nicely also but may not be sufficient on its own in a very cold climate.

Thank you very much for the response!

i rent in a duplex with a car port big enough for 1 car and no trees. So the patio out back houses the cold frame. The heat cable provides constant heat for the trees when needed. During the night when the cable is on it keeps the trees pots ambient temperature around 35-50 degrees. I bought a electric thermostat that will supply power to the heat cable when the temp drops below 35 and turns the cable off when temp exceeds 45. That will be the ideal temp for these trees.

Your set up may work fine for maintaining the proper night time temperatures but you want to watch out for the cold frame overheating - exceeding much more than 45F - during the daylight hours. Sun - even winter sun - can heat things up a lot with plants under plastic or glass.

Ok well thanks for the info, I will look into what the temp is in the actual cold frame during the day.