The first thing to do when troubleshooting a heat pump is to change the battery in your thermostat. You will need one of the batteries listed above depending on the model of Coleman heat pump. If the heat comes on after you have changed the battery, then your problem is solved. If not, you will need to move on to the next step.
Try a manual override. Remove the cover of your heat pump thermostat. It should snap off easily. Locate the override switch underneath the cover. When you push the switch, it will manually complete the circuit for the heat pump to run. If the heat pump runs when you push the override switch, then you have learned that the thermostat is broken. It will need to be replaced by a professional. If it does not run when the switch is pushed, then move on to the Coleman heat pump unit itself.
Remove the cover on the unit outside your house. Use the screwdriver to remove the screws, which you should place in a location you can find easily once you are done. The heat pump coils will be exposed once you remove the cover.
Troubleshoot the heat pump coils by cleaning them. Wear your gloves and use your whisk broom to clean off debris on the coils. Turn the unit on and see whether there is any difference in the heat that is created. By cleaning the coils, you may have solved any problems you had with your unit.
Check out the fan function on your Coleman heat pump. If you turn your unit on and the heating/cooling fan is not spinning, that means the bearings on the motor are bad. These will need to be replaced by a professional. If the fan is spinning, then the compressor is broken and will also need to be replaced by a professional.