Why don't heat pumps run for a bit BEFORE starting the air circulation fan?
I don't think the problem you're having would be solved by a fan delay.  When the fan turns on, it has to purge all the "cold" air from the ducts, before the warm air reaches the registers.  There's not much that can be done to solve that problem, other than having really short duct runs.

If you did add a delay, the system would likely overheat.  This could cause a bunch of problems, as well as reducing efficiency. 

If you did want to add a delay. It would require a thermocouple and relay, or a time delay relay.  I doubt your furnace has any firmware, unless it's a super fancy custom system.