My 4 ton year old heat pump unit delayed 25 minutes before coming on this morning. The unit heated until thermostat setting was reached, then stopped. However, it restarted and ran several times at short intervals while the thermostat remained at it's set value. This is the first time that I've noticed this behavior. Could this problem be related to my thermostat - it's a 10 year old Honeywell non-programmable heat pump compatible thermostat.

Sure the thermostat could be the problem and there are ways to check it depending on the model. It's a cheap and easy fix. Need a link? Provide model and number.

https://www.youtube.com/watch?v=81_gCF4mJtQ

Hope that is indeed the problem. Unfortunately there could be many other problems only a very knowledgeable person or professional could solve.