"On my existing T-stat, the heat is set to come on at 6:00 am. One morning I decided to see how the system would perform if I turned the fan on at the same time running continuosly, and it seemed that the furnace was cycling less than usual. I thought if I could program the fan to stay on from 6-9 am ( the same time when my heat comes on in the
morning) it would help save energy. "
I'd be surprised if this saved any energy. For one thing, running the fan consumes a good bit of electricity. For another, you are running warm house air through ducts which in most cases run in areas like basements that are unheated. And every duct system I've seen has some leaks, so some of the warm air is going to be lost into areas like the basement on it's many trips around the block.