# Newton cooling in different media

I performed the simple Newton cooling experiment where I have a body of known surface area $A$. If I heat it and then place it hanging from somewhere, so that it is in contact only with air, it will cool exponentially. Here I am able to measure the thermal conductivity of the material $h$, where $k=Ah/mc$ ($m$ the mass of the object and $c$ it's specific heat), and the temperature decreases as $e^{-kt}$. Now, from the construction of the Newton's model

$$A^{-1}\frac{dQ}{dt} = h(T-T_a), \quad \quad \quad \quad dQ=-mcdT$$

I never take into account the medium that absorbs the heat from the body. Of course $h$ is not the thermal conductivity of the material, since it depends on the material of the body, and also on the material of the medium. How can I extract information (i.e. some coefficients of thermal conductivity) from the medium and from the body separately?

I appreciate your help.