The stability of Al-Mn transition edge sensor (TES) bolometers is studied as we vary the engineered TES transition, heat capacity, and/or coupling between the heat capacity and TES. We present thermal structure measurements of each of the 39 designs tested. The data is accurately fit by a two-body bolometer model, which allows us to extract the basic TES parameters that affect device stability. We conclude that parameters affecting device stability can be engineered for optimal device operation, and present the model parameters extracted for the different TES designs.