A Thermal Ohmmeter

It doesn't have to be self heating, but it helps a lot: thermal circuits are much less perfect than electrical ones, and you have to take into account all series parasitic resistances (equivalent to copper wires in the electrical domain) and thermal leaks due radiation or convection (equivalent to insulation resistance).

Here is a sketch of an ideal situation, where you can make your measurements in an electrical fashion, and a more realistic one (simplified).

In order to determine the thermal resistance of the sample, you need to accurately determine the effective thermal power flowing through the sample and the temperatures on both sides.

In an ideal world, it looks simple enough, but when you look at the more realistic situation, things become much more complicated.
The problem is not the amount of arithmetic corrections required, but determining them exactly, using some calibration method.

When you have lots of unknowns, the task becomes increasingly difficult, and having the sensor and heater separated only by a few microns of silicon helps a lot.

A possible alternative would be the use of a small block of copper or silver as a proof specimen, with the heater and thermal sensor bolted to it.
I considered this option, but in the end I preferred the combined sensor/heater because the thermal leaks directly to the ambience were much smaller: only one device, against two, plus the block itself and the connecting wires.

Even with the smallish SOT80, I had to include a compensation for the direct Rtj-a leak of the case, but it was relatively minor.
With a larger assembly, the leaks would have been more important, making the compensation more critical: subtracting quantities is not the best way of optimizing your uncertainty total
 

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For increasing the accuracy of the calorimetry you could use guard rings to ensure the measured heat flow was uniaxial. With enough budget diamond heat-spreaders might be handy? You can sandwich the heating element between two stacks of sample so that there is no heat loss from the other side of the heater. Pt resistance probes would be needed for really accurate work too.



Its cheaper and easier to just calibrate from known samples though, and have a crude model of heat losses and errors. After all most materials have thermal conductivity that varies with temperature somewhat, are you going to measure that whole curve, or just a representative value at a realistic temperature?
 
For increasing the accuracy of the calorimetry you could use guard rings to ensure the measured heat flow was uniaxial. With enough budget diamond heat-spreaders might be handy? You can sandwich the heating element between two stacks of sample so that there is no heat loss from the other side of the heater. Pt resistance probes would be needed for really accurate work too.
This is just a DIY project, not a true lab instrument, and materials like diamond are way over the top.

If people from Tektronix or Keysight wanted to build such an instrument, the first and most important step they would take is to develop a dedicated sensor/heater: something like the SOT80, but with thicker sole incorporating a precision temperature sensor and occupying the full area of one face.




are you going to measure that whole curve, or just a representative value at a realistic temperature?
Due to the construction, one side of the material will always stay ~at room temperature, and the other will heat to a point determined by its thermal resistivity: a bit like the real use situation, but more extreme, because in reality, the heatsink will heat up, reducing the temperature gradient.

Anyway, there should be no phase change for the usual insulating materials in this temperature range, meaning the changes should be moderate and gradual.

In its current form, this instrument only provides indicative absolute values, but it is sensitive and repeatable enough to make meaningful comparisons, which is the main goal.
For example, this enabled me to produce and perfect sheets of high-performance insulators based on MgO:
ELEKTR⚡A is a true High-Voltage lab supply, truly DIY-friendly
 
Yes, it is certainly an interesting possibility, but it would be difficult to implement at a DIY level.
For an institution, buying the sensors, instrument and software bundle is the way to go, but if you buy the sensor alone (the affordable option for the DIYer), you need to create not only the physical interface but also the driving and number-crunching software to create the stimulus and extract the results.

It is by no means an impossible task, but you have to know all the sensor parameters, and I am not sure they are easily available publicly.

A starter kit, with conductivity calibration samples seems to cost about 6,000$:
THERMAL CONDUCTIVITY KIT



– Thermal Conductivity Kit

This is still within the reach of a determined DIYer, and it is probably possible to find cheaper alternative on Aliexpress for example, but steady-state methods are much more affordable and do not need to rely on external sources of calibration or data.

A hot-wire method, for example with a disposable single wire or loop of platinum wire would probably be possible, cheaply and without requiring other data than fundamental constants.

It would require serious math and programing skills to extract the results though, but some of the forum members certainly have them