Sounds like the units you are describing don't have an efficient (read 'big enough') heat-exchanger which is why they aren't being effective in not-so-low temperatures. The temperature of the cold-side should not be below outside ambient temperatures if the heat exchanger coils are sufficient.

In other words heat-energy should be going into cold side of the heat-pump (even at a low temperatures) at the same rate as it is coming out the hot-side at high temperatures. Reduce the heat in, and you will reduce the heat out.