New here...

[steveo]

how high does your temp gauge read?

possible someone put the wrong thermostat in this thing?

the lt1 thermostat is special, an SBC thermostat fits but it acts strangely like that.

also a good thermostat is designed to stick OPEN in failure mode, which may be what has happened here.

in 20 minutes your heat should be blowing deadly hot. this is not a tune issue. and a cold running car will not only lose fuel economy because of efficiency, but also deposit accumulation due to never getting hot enough to burn all the crap out of the top end.

however, you need to flush your heater core reguarly on an LT1, due to location, flow direction and strength, and dexcool sludge, they clog up often. 15 minutes of hose water through each side of the heater core seems to do it.

just some ideas

[steveo]

read all this stuff:

heater core flush: http://shbox.com/1/4th_gen_tech2.html#heaterflush
thermostat location, and correct/incorrect part comparison: http://shbox.com/1/tstat.jpg
cooling system overview, and a good refill/bleed procedure: http://fbodytech.com/coolingsystem.html

[notsue]

Replaced the motor in 2012 and flushed the heater core that year also and that's why I get super hot air now... Before the flush it'd never blow hot even if the car was at temp. I know I replaced the thermostat around the same time also, but no idea which one I put in it. Will have to check. I'm still just using the factory gauge until I can decide where I want to put aftermarket gauges.