Your heat pump needs to be sized for the size of your property and the temperature differential that the pump has to cope with.
For example, if you have a heat pump that can store enough heat to give you 3 months worth of energy that takes your property to above freezing point (having to raise the air temperature by 10 or 15 degrees Celsius) and you only then need the energy to take the room temperature to one that is comfortable.
You would need to research heat pump designs, work out how much your current energy consumption is and how much you will save from having one and how much this saving is, you then know how fast you recoup your outlay.
Your climate will play a big part in how much energy you can store and save. If you know locally in your area, people who have heat pumps, you can get it from the horses mouth...