Need more information. Why did you change the thermostat?
What is the brand and model number of your furnace.
If it worked for awhile it might be just a loose connection.
The furnace, a coleman 3800, sometimes blows hot air and sometimes it blows cold air, could it be the thermostat, although it was changed recently, it seems there's not catch from the thermostat
It sounds like you have a intermittent problem so it could be just about anything.
If your furnace has a flame sensor try cleaning it.
Look at the sticky notes at the beginning of this board for more info.
Is this in a mobile home?
Is this in a travel trailer?
I have no listing for a 3800 series Coleman.