Actually the Thermopads only offer adhesive over top of the sensor with an access hole in the middle. If electrical insulation between sensor and device is needed, then cpu type 3M thermal tape is the best. to get good thermal bonding, in which case, the Thermopads are almost useless as any polyamide tape such as Kapton, over top can be used with 3M thermal tape (thinest possible) to provide electrical insulation. Thermocouple drivers are often ungrounded so insulation is not necessary. But shield might be necessary, especially if there is a lot of EMI from say PWM drivers or inductive currents nearby. This is usually alum foil over twisted pair.
But when it comes to measure LED temperatures, one does not even need a thermocouple, the Diode itself is a thermal sensor. All it needs is calibration with power off or so there is no temperature rise until a pulsed current is provided using say a sawtooth current generator with a DSO to measure then apply your knee current say 1% of rated current up to operating current in design, so you can measure the Vf and If and know exactly what temperature the LED passively heated in an oven. This information is pretty useful for all kinds of things. You essentially get the model of the Vf and ESR both as a function of If, so you can determine the temperature of the device later in different environments and see if the heatsink interface has drastically changed thermal resistance from expected values or the diode ESR has degraded significantly, without having to instrument up every device. There will be a learning curve to calibrating the tolerance factors between batches of devices, just as ESR improves over long term process improvements, escapes pop up with high ESR that may be damaged from some event.
So you essential confirm the device is typ. -3mV/deg 'c if that is what is in the spec and then the ESR vs I and vs T to small extent and get to see the LED performance .
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I have been laboring this topic for some time, but as ESR critical in Capacitor, Batteries and Inductors, also it is critical to understand the behavior of ESR and Vf with current & temp. YOu can expect 1% temperature accuracy from a standard low current thermal sensor, and you can expect the same accuracy from a large LED albeit, it will react slower and be more sensitive to offsets due changes in cooling effects from air flow effects on heatsink. When you have mastered this, you can easily drive "some" LED's" in parallel with drivers and wire resistance with much smaller drops than a current source... read much more efficient. But no one is offering such drivers yet. It's complicated, but I expect when efficiencies must improve over the rival Fluorescent lamp with simlar or better efficacy, this is one way to do it.