"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.