Ever since having a new furnace installed, it has never actually put out HOT air... it blows cool air, gradually warming, but never actually warm. Until the fan stops, and then some warm air trickles out of the duct

That is a gas model abd should put out enough heat so you can feel a difference. It could be the unit needs adjustment to the gas valve pressure so it will perform properly. This should be done by a professional and if it has not worked properly since installed the company that put it in should come back and take care of business.

New furnace installed should have a warranty,, call the installer,something is just not right