Weakly Interacting Massive Particles (WIMPs) are candidates for non-baryonic Dark Matter. WIMPs are supposed to interact with baryonic matter via scattering off nuclei producing a nuclear recoil with energies up to a few 10 keV with a very low interaction rate of ~10^(-6) events per kg of target material and day in the energy region of interest. The Dark Matter experiment CRESST (Cryogenic Rare Event Search with Superconducting Thermometers) and the EURECA project (European Underground Rare Event Calorimeter Array) are aimed at the direct detection of WIMPs with the help of very sensitive modularised cryogenic detectors that basically consist of a transition edge sensor (TES) in combination with a massive absorber crystal. In the CRESST experiment the search for coherent WIMP-nucleon scattering events is validated by the detection of two processes. In the scintillating absorber single crystal, CaWO_4, heat (phonons) and scintillation light are produced and detected with two independent cryogenic detectors: a phonon channel and a separate light channel. The development of such cryogenic detectors and the potential ton-scale production are investigated in this paper. To decouple the TES production from the choice of the target material in order to avoid heating cycles of the absorber crystal and to allow pretesting of the TESs, a composite detector design (CDD) for the detector production has been developed and studied. An existing thermal detector model has been extended to the CDD, in order to investigate, understand, and optimize the performance of composite detectors. This extended model, which has been worked out in detail, can be expected to provide a considerable help when tailoring composite detectors to the requirements of various experiments.
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