2000 Chevy Venture Heater does not blow warm air.

How did they check the t-stat? One sure way to check for intake or head gasket leak is to look at the bottom of the oil cap. If you see a milky looking gook on it then your getting coolant into the oil. Another way if the motor is burning the coolant there will be steam in the exhaust and if you take your bare hand and put it close to the tailpipe with it running you won't be able to hold it no closer than 3" without it burning you hand. Also should be a whitish smoke from the tailpipe[not always but most of the time] are you loosing any coolant and having to put somemore in? If no coolant loss then could be the fresh air damper not working properly and instead of closing it is still letting cold air in it is in the passenger side heater box but the lines are where they can be seen. And you can listen if it is moving by moving the temp control.