2005 gtp with remote start

[ZR1Vette09]

Actually, my thought was that it reads the outside temperature and adjusts accordingly.

[BillBoost37]

Having recently installed a Viper 5901 into my 00 Regal, the basic principles of how this should work is that the remote starter powers up the wiring that gives the climate control and blower motor power. From there the climate control uses it's settings to heat/cool the car as it sees fit. Now with that out of the way... let's ask some further questions.

Is this your first cool season with the remote starter?
Who installed it?
Not being familiar with the 05, I'd suggest checking the schematics to ensure the ambient (exterior) and interior temp sensors are being read by the climate controls when the remote is on. It might be that the circuit that supplies power/ground to the sensors isn't active and it's defaulting on cooling. The minute you put the key in and give the rest of the systems power, the sensors come alive and you get heat.
Maybe the actuators that control temp aren't being powered.
There are a lot of possibiliies which is why I ask...who installed it.