If stopped by the POPO, this is my recommendation (and what I do, Cops get stopped too, we tend to have heavy right feet).
Windows down... all of them (we might be making a passenger approach). Palms up on the steering wheel (shows nothing in hands and both in sight). DONT go fishing around for your wallet on your way to the shoulder (from our view it looks like you are hiding or accessing something, something that might hurt us) , or after you came to a stop (for the same reason) , wait for us to say hello first. You might not need the stuff in the first place (we put you on the curb to tell you your gas cap was off as an example). Be polite as we should be doing the same, and the stop will be over quickly.
Now if you have the heater in the car or on your person (post getting your LTC) ..If your particular heater is within reach of you when you get stopped, my advice is Advise the officer that you are armed and where it is (your drivers license is going to tell us if you have an LTC anyway) . When I worked patrol I always appreciated the update and usually said a variation of what was posted earler "You dont go for yours and I wont go for mine" with a smile.
If your gun is where you need to access TELL us "My gun is in the glovebox where my insurance card is, what do you want me to do?" we will be clear on what we want to happen. In Texas the registration system may tell me you have insurance anyway (its getting better but not anywhere near 100% accuracy yet)