Specific heat is one of the most powerful thermodynamic probes of quantum materials, providing direct information on low-energy excitations and phase transitions. Conventional calorimetry, however, requires samples that are well isolated from the environment and typically of millimetre dimensions and tens of milligrams in mass. For many newly discovered quantum materials – especially strongly correlated compounds and designer heterostructures grown as thin films – high-quality single crystals are only available in extremely restricted volumes, making their heat capacities, often in the sub-nJ/K range, inaccessible to standard setups. At higher temperatures, membrane-based calorimeters can partly address this challenge, but the key limitation for the regime most relevant to quantum materials remains accurate thermometry under high magnetic fields and at ultra-low temperatures. In this seminar I will introduce a nanocalorimeter based on Coulomb blockade thermometry (CBT), in which Al/Al₂O₃/Al tunnel junctions are suspended on SiN membranes. CBT offers a primary, in-situ calibration mode and is intrinsically field independent, enabling reliable thermometry down to the mK range in large magnetic fields without time-consuming calibration runs. I will show how this approach allows us to measure the specific heat of microscopic single crystals of the unconventional superconductor CeRh₂As₂. These microcrystals exhibit significantly sharper transitions and higher onset transition temperatures than mm-sized samples from the same growth, allowing us to resolve the multiple superconducting phases and their interplay with a density-wave state with previously uanvailable thermodynamic precision. I will close with an outlook on how this technology can be extended to spin-liquid candidates, heavy-fermion thin films, and other fragile quantum materials whose thermodynamics have so far been out of experimental reach as well as its potential to obtain thermodynamic measurements on few-layer thick membranes.