[en] The energy sensitive detection of energetic heavy ions with calorimetric low temperature detectors is investigated. The temperature readout was done with an aluminum transition edge thermometer operated at T∼1.5 K. For ²⁰Ne-ions with an energy of E=100 MeV/u from the SIS accelerator at GSI Darmstadt the best energy resolution obtained was ΔE/E=1.9x10^-3. This value corresponds to the energy spread of the ion beam of the SIS. In a first application of such detectors the excitation of the giant resonance in lead nuclei via the reaction ^natPb(²⁰Ne, ²⁰Ne)^natPb* was investigated by separating inelastically from elastically scattered ²⁰Ne-ions in the energy spectrum. At a scattering angle Θ_Lab=3 the excitation energy and the strength of the giant resonance were found to be in good agreement with theoretical predictions. In a first test with an exctracted cooled ²³⁸U-beam with an energy of E=3600 MeV/u from the storage ring ESR with an intrinsic beam energy spread of ΔE/E≤2x10^-4 an energy resolution of ΔE=97 MeV (ΔE/E=1.1x10^-3) was measured. The baseline noise was ΔE=17 MeV. Further improvement of the energy resolution seems possible. (orig.)