The voltage across R1 is indeed used to determine the current limit...................will R1 get hot during current limiting ? all in know LM317 is acting as a voltage regulator and of course will get hot , but which component is responsible for current limiting ?.............
Power is I²R, thus the maximum power dissipated in R1 is 1.2² * 0.1 = 0.144W so a ½W resistor would be more than adequate.