I bought a house with a heat pump system in Summer 2010. Due to the winter, the temp dropped now below 32 degrees. The heat pump provides sufficient heat, and it seems the pump itself is running only if necessary.
I recognized that the inside fan/blower however seems to run constantly and only shuts off seldom. The electricity bill was significanty up in November, even it was already cold, but it looks like the December usage is double than November.
Is it normal that the inside fan/blower runs almost 24h, but not the heat pump? If not, what might cause the problem?

I have an older T-stat with I can set to heat, Emergency heat, cool, and OFF, plus Fan to AUTO and ON. It has 3 status lights, one for Aux heat (I assume that is the heat pump), one for Emergency heat, and one for “Check”.

Actual outside temperature is about 30F during the day and around 10-20F during the night.
I have set the T-stat to 72F. The outside heat pumps runs for a while (maybe 10 minutes) and than turns off. While running, the "Aux Heat" light on the T-stat is on. The system provides warm air inside the house.
The inside blower blows almost 95% of the time, even when the heat pump stopped.
If I reduce the temp of the T-stat to 70 or 69F, the inside blower stops for a short amount of time (5-10 minutes) and then starts over again.

I assume the relay is OK, and that it is normal that the inside blower blows almost all the time to keep the temperature? I have checked the heat pump inside unit and there is no visible control to set the blower temperature.

Can someone confirm that my system is working properly and that I have to suck it up that the inside blower is running constantly during winter times, resulting in way higher electricity bills?
Would it make sense to replace the old T-stat with a new, electronic one? Would that help to stop the blower running constantly?

Thanks
Martin