An MEMS pressure sensor is designed to reduce or eliminate thermal noise, such as temperature offset voltage output. The pressure sensor includes a pressure sensing element having a diaphragm, and a cavity formed as part of the pressure sensing element, where the cavity receives a fluid such that the diaphragm at least partially deflects. The pressure sensing element also includes a plurality of piezoresistors, which are operable to generate a signal based on the amount of deflection in the diaphragm. At least one trench is integrally formed as part of the pressure sensing element, and an adhesive connects the pressure sensing element to the at least one substrate such that at least a portion of the adhesive is attached to the trench and redistributes thermally induced stresses on the pressure sensing element such that the thermally induced noise is substantially eliminated.