Heating up using an LM317 voltage regulator
Yes, under the conditions you are using the regulator, it will heat up a lot, as it is a linear regulator. It will dissipate all excess power as heat.
Since the voltage over the regulator input and output is about 8V, and the maximum current draw is about 0.2A, the regulator will have to dissipate maximum of 1.6W as heat.
The junction to ambient thermal resistance is about 25 degrees C/W, so as an extremely crude approximation, chip case can be approximated to be about 40 degrees higher than ambient room temperature.