Many high-temperature superconductors in their normal state show marked deviations from the Fermi liquid theory. The most prominent is a linear-T dependence of the resistivity which can cover a broad T-range and even cross the Mott- Ioffe-Regel limit. Such unusual behavior is believed to indicate the destruction of quasiparticles caused by the presence of a quantum critical point (QCP) inside the superconducting dome and to play a key-role in understanding the emergence of high-temperature superconductivity in such materials. In order to follow the destruction of quasiparticles and to understand its relation to the QCP, it is crucial to study the thermodynamic and thermal transport properties of quantum critical systems, which have so far received much less attention than the more easily accessible resistivity. Here we report our development of a heat-pulse calorimeter suitable for small single crystalline samples, a T-range 300mK–300K and fields up to 38T. We also present our first results on FeSe1-xSx, a family of superconducting materials with a nematic QCP.