how to switch a LM317 voltage regulator / LED on and off?

Good. Sounds like you've got the hang of this.

MarkT:
And don't forget the heatsinking for the LM317, it'll draw about 5.5W and the 1.8 ohm resistor will dissipate 0.9W remember.

Does that mean the LM317 heatsink should have a Thermal Resistance of 6.6 °C/W?

Thermal Resistance = (60 - AmbientTemp) / Power
Thermal Resistance = (60 - 20) / 5.5
Thermal Resistance = 6.6

Those things are huge!

That's a bit of overkill.

With a supply voltage of 7.5 @ .7 amps, the LM317 will be dissipating:
WD = 0.7 x (7.5 - 3.8 - 1.25), or about 1.7 watts. Let's call it 2 to be safe

They recommend a maximum TJ of 125°C for an LM317, but let's keep it cool and on the safe side at 85°C to factor in junction to case RT. And we'll put ambient at 25°C, again to be safe. Then we have:

RT= (85 - 25) / 2, or about 30°C/W should do nicely.

Would it also be possible to dim the led by using PWM on the transistor?

Btw: I'm really new in this world so if I say stupid stuff... please forgive me.