Temperature monitoring plays an important role during thermal treatment of diseased tissue. Ultrasound (US) can be used to estimate the temperature and one common approach is based on the local detection of instantaneous frequency changes in reflected US signals along the axial beam direction. Herein we propose a novel US-based temperature estimation technique that improves on this established method by filtering the reflected US signals with Gaussian-weighted nth-order Hermite (GHn) polynomial functions. This filtering step helps isolate the US signal from tissue structures while minimizing presence of degrading signal components. In vitro experiments were conducted by slowly heating a series of tissue-mimicking phantom materials that were fabricated using hydrogels embedded with US scatterers. US data were collected using a programmable research scanner (Vantage 256, Verasonics Inc) equipped with an L11-4v linear array transducer and processed offline to extract local temperature estimates. Overall, our US-based temperature mapping technique exhibited improvement in measurement accuracy compared to the more US-based approach.