Heat Pump - Cut off compressor at certain temperature?

Is there any logic to setting a heat pump to run strictly on emergency heat when the outside temperature drops below a certain temperature? I had a a minor repair done and the technician suggested that I might want to install a device that would, in effect, disable the outside compressor when the temperature dropped below a certain point.

I have an addition on my house that is heated by a heat pump. It's a relativly small space (about 600 SF). The heat pump is an energy hog in the winter and I'm looking for ways reduce my electric bill.
The rest of my house is hot water base board & radient underfloor heat, but it would be very difficult to extend that system to the addition.

There is less and less heat in the outside air as the temperature drops, and thus, the heat pump has less and less to actually move from outside to inside. SO, depending on its efficiency, at some point, it will not be able to extract any heat, so yes, at some point it becomes cheaper to just use the emergency heat, as the cost to run the compressor and the heat extracted starts (eventually) to become a negative factor - i.e., you'd get more heat by just running the resistance heater strips for the power expended. Now, the newer units are more efficent than older ones, and the point at which they no longer are capable of running and extracting heat is lower than older ones. Somewhere in the spec sheets of the unit you have, they will discuss that cross-over point, and it becomes more efficient to just run the emergency heating. They may also have some charts. You have to figure in your local electrical rates, too. Some places give you a break on electricity if used for heating verses 'general' use, so there may be a tiered structure that makes the calculation harder.