If you are interested only in relative temperature changes with different LED controls what you are doing is on the right track. As Ian stated, there will be heat conduction into the thermocouple wires which can be reduced by using the smallest available thermocouple wires and making sure there is the best possible thermal connection with the relatively tiny measurement location.
Some good thermal compound that is not electrically conductive at the measuring point will help; but if it is electrically conductive, it will throw off the thermocouple readings. I can’t tell from your picture, but you may already have thought of this.
Do not solder the thermocouple. Thermocouples generate a tiny voltage at the junction of two dissimilar metals and solder would in effect short out the output at the source.
I see kapton tape covering a lot of the heatsink; if you are attempting to test the LED and heatsink combination, it would be better to make a little dog clamp out of non-conductive material (plastic, fiberglass, etc.) that would hold the tip of the thermocouple in place and hold the LED module against the heatsink at the same time.