Accurate temperature estimation of high density active power electronic systems is vital for dynamic thermal management. Accurate and reliable estimation is especially important in regions that are close to failure, either due to high temperature or significant materials or component sensitivity. Improved estimation can support lower safety factors and enhanced system performance. An investigation of optimal temperature sensor placement methods is presented here, focusing primarily on methods utilizing information-based metrics. In addition, physics-based metrics are explored in an initial study that may have the potential to be more closely aligned with overall system utility. Studies are based on a 2 kW, single-phase, seven-level, GaN-based inverter. A lumped-parameter reduced-order thermal model, developed in previous work, is used for real-time temperature estimation. A continuous relaxation of a 2D placement domain led to a novel linear programming formulation that supports solution of finely-discretized sensor placement problems with minimal computational expense. Improved sensor placement performance metrics account for multiple loading conditions and estimation accuracy with respect to failure prevention.