Usually lock-on grips just slide on, no warming required.
Unless you are dealing with superlight MTB handlebars, it doesn’t matter too much whether the locking collars are in or out. Some grips are meant to have them inside, some outside. Modern carbon bars usually have enough wall thickness to accommodate the pressure of the collars at both locations.
Just tighten the collars enough to not twist when you are riding. I would start around 4 Nm and snug up to 5 if needed.