High purity single crystalline calcium fluoride ($CaF_2$) has excellent optical transmission characteristics down to deep UV and is therefore selected as the main optical material for the next generation of lithography apparatus operating at wavelength of 157 nm. The growth of large sized $CaF_2$ single crystals with the required properties for this optical application can be achieved only by optimizing the crystal growth process by the aid of numerical simulation. This needs especially a precise calculation of the heat transport and temperature distribution in the solid and liquid $CaF_2$ under crystal growth conditions. As $CaF_2$ is considered to be semitransparent, the internal radiative heat transfer in $CaF_2$ plays an decisive role in the simulation of the heat transport. On the other hand it is very difficult to obtain quantitative experimental data for evaluating numerical models as $CaF_2$ is extremely corrosive at high temperatures. In this work we present a newly developed experimental technique to perform temperature measurements in $CaF_2$-crystal as well as in the melt under conditions of crystal growth process. These experimental results are compared to calculated temperature data, which were obtained by using different numerical models concerning the internal heat transfer in semitransparent $CaF_2$. It will be shown, that an advanced model, which was developed by the authors, gives a much better agreement with experimental data as a standard model, which was taken from the literature.