Because thermal transport determines the dynamic and static operation of bolometric detectors, control of the thermal conductance is critical for the implementation of detectors utilizing superconducting Transition Edge Sensors (TESs). For this reason, we have examined the use of partially perforated membranes for thermal management. This technique preserves the physical integrity of the membrane, and therefore maintains the mechanical robustness of the detector. This paper describes investigations of the thermal transport in trenched membranes. The test configuration consists of Mo/Au TESs lithographically defined on silicon nitride membranes 1 micron thick, 6 millimeter square in size. Trenches with variable depth are incorporated between the TES and the silicon frame in order to control the thermal transport. We demonstrate the ability to reduce the thermal conductance by a factor of ∼3 or greater using this technique. [ABSTRACT FROM AUTHOR]