Have you checked the coolant level and that the engine comes up to working temperature?
If they are both OK the heater is a full flow system so I would suggest its the air flow distribution that is not swapping from cold overto passing through the heater matrix, don't know whats involved insorting that out, could be electrical instruction or mechanical failure.
Do you have the screen clearing mode on? With climate controlthat engages the air con and makes it chilly! In my experience you have a choice- be able to see where you're going or freeze! Incidentally, there is no such thing as a 2007 LTZ- LTX with the wrong badge (the LTX badge is routinely replaced with LTZ of the tailgate is repainted as it doesn't appear on the Chevy parts list- its a Daewoo part...).
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