I leave my temperature control in the Auto mode. When I start the car up, the air seems to blow with a lot of force....cold air that is. After a few minutes, the the force of the air dies down

In other cars, the fan would not run for a few minutes until it warmed up, and then the fan would start up. Now I just get a nice long blast of cold air.

Is this how it is supposed to work on the GC SRT?

I believe it shouldn't come on for a few mins. I'd take it to the dealer, there may be a TSB.

depends on what temp its on

Mine never does that. I leave in full auto mode all the time and it's always started out with the fan on a slow speed. Might need to have that looked at.

...Is this how it is supposed to work on the GC SRT?
No, in auto mode it should not start blowing air until the engine warms up.

The air blows based on the temperature in the interior. If it's warmer inside than the setting of the climate control, it will blow cold air immediately, regardless of temperature outside and regardless of engine warming up. If it's colder inside than the setting of the climate control, but cold outside with a cold engine, it will not start blowing warm air until the engine warms up. In either case, after a few minutes, the rate of air blowing should level out. I have had climate control on several other cars and it always works this way.