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What physical for and geometies are you talking about? How big are the samples? Heat transfer experiments can be pretty simple if you are talking about measuring the thermal conductivity of a long bar or a brick but if it's some 5mg sample of a compound then you will have a great deal of difficulty taking accurate measurements due to equipment limitations and such.
If you have a sample large enough, then insert a thermocouple inside of it and immerse the room temperature object into a large (so you can model it as an 'infinite' heat sink) fluid (preferreably water) and measure the time it takes for the object to reach an equilibrium temperature with the surrounding environment. With proper use of the methods of time-dependant conduction in your heat transfer book, you should be able to measure the thermal conductivity.
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