Furnace is blowing cold air, changed thermostat, worked for a while, but now it's back to blowing cold air

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 brand name is Coleman 3800

Its not blowing hot air, just cold air

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.