Unless it's specifically labeled maximum junction temperature, operating temperature typically means case (package) temperature.
The datasheet (
http://www.seoulsemicon.co.kr/_homepage/home_kor/product/spec/X4218X.pdf) contains all the data you need, you just need to examine it closely.
The maximum operating temperature is going to be of the LED case, which is specified at 85C. The maximum junction temperature is 145C, but only if you run at less than 700mA. Above that to 1000mA, you must keep the junction temp below 90C.
Seoul specifies the Junction -> board thermal resistance for a star board at 8.5C/W, while the junction -> case (which would be no star board) at 6.9C/W. So the star introduces 1.6C/W of thermal resistance.
So let's put it all together.
You measured 125F behind the star, which is 52C
The aluminium + thermal interface to the star adds about 1C/W
So thermal resistance from your measurement point to the case is going to be about 2.6C/W.
Thermal resistance from your measurement point to the junction will be about 9.5C/W
We want to be conservative, and simplify the math, so let's call it 3C/W and 10C/W respectively
At 500mA, the Vf of the Seoul is probably around 3.4V. The LED is dissipating about 1.7W.
So the case temperature is going to be 52C + (3C/W)*1.7W = 57C
You're fine there.
The junction temperature will be 52C + (10C/W)*1.7W = 69C
Everything looks good there as well.