I agree with pwillard and thanks for a reference diagram.

What is your supply voltage and load.

The sense resistor will only dissipate a constant energy, the 317 will dissipate the rest depending on what the resistance of your load is.

If the resistance of your load decreases, ie conducts more current, then the current through the sense resistor increases and so the volt drop across it increases, to keep 1.25V across the sense resisitor the 317 will decrease its conductivity to drop the current back to the set level. The out come of this is that the voltage drop across the 317 output to input increases, with the same current this means that more power is dissipated in the 317.

If the resistance of your load increases, ie conducts less, then the current through the sense resistor decreases and so the volt drop across it decreases, to keep 1.25V across the sense resistor the 317 will increase its conductivity to increase the current back to the set level. The out come of this is that the voltage drop across the 317 output to input decreases, with the same current this means that less power is dissipated in the 317.

As you will not in each case the current at all times through the sense resistor will be the same as will the voltage across it, so will its power dissipation.

If you want a variable current limit then you will have to go into more elaborate circuits.

Tom