A condensed excitonic phase has been realized in intermediate valent TmSe0.45Te0.55 at low temperatures and high pressures. In this paper we report for the first time about some thermodynamic properties such as the heat conductivity and the thermal diffusivity which have been obtained between 300 K and 1 K and between ambient pressure and 17 kbar (1.7 GPa). Pressure and temperature are used to navigate in the intermediate valent semiconducting phase, in the condensed excitonic phase and in the intermediate valent metallic phase of the complete phase diagram. In the condensed excitonic phase the heat conductivity λ of the excitonic phase increases exponentially below about 20 K suggesting a superthermal current for T → 0. In a solid this has never been seen before. Also the thermal diffusivity a strongly increases below 20 K, giving evidence for second sound.