heater blowing hot then turns cold, checked furnace codes...they are okay

Should I replace thermostat?

Turns cold and keeps blowing or blowing hot, then cold(er) air for awhile and then turns off?

blows hot, turns cold, then I shut off

So, does it reach the set temperature? I suspect this isn't the thermostat, but a control board issue. Check here for similarities with your situation:

it usually will reach the set temperture, and doesn't do it all the time...it's a coleman furnace serial number w0n9454962 model tg9s080b12mp11a

last serviced 1-7-10

If this is intermittent, I would check the air filter, too - the furnace may not be able to achieve a steady state and shuts down prematurely (though may feel like it's about to reach the set temperature,it may not be actually there, and you will not hear the thermostat click or see a change on its display). It may be having a problem moving enough air and shuts down for safety.

Try a thinner air filter (simple fiberglass air filter, no special anti-bacterial or anything like that) and check the registers for any that may be blocked unnecessarily. For testing might even run it without the air filter and see if it improves, then get a thinner filter that creates less resistance to air flow.

pressure switch open/closed. easy to replace i hope...