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The effect of substrate thickness and its Debye temperature on the bolometric response of the freestanding-membrane type of superconductor transition-edge detectors is investigated. The investigation is based on the calculation of the variation of the specific heat per unit volume and the heat conductivity using the finite-size scaling method for different Debye temperatures and micron size thickness of substrate. We also calculated the heat capacity and time constant for various materials with Debye temperatures in the range of 600-1400 K. The calculated results are compared with previously reported response values obtained theoretically and experimentally for the thermal-based infrared (IR) detectors. The IR response versus substrate thickness of these types of devices for different modulation frequencies is also presented. This inspected response at low thicknesses of substrate shows anomalistic behavior with respect to the previously reported results of response analyses. Here, we also obtained the optimized substrate thickness and Debye temperatures for maximum responsivity of these types of devices.