The integration of smart thermostats in home automation systems has created an opportunity to optimize space heating and cooling through the use of machine learning, for example for thermal model identification. Nonetheless, its full potential remains untapped due to the lack of a suitable learning scheme. Traditional centralized learning (CL) and federated learning (FL) schemes could pose privacy and security concerns, and result in a generic model that does not adequately represent thermal requirements and characteristics of each individual home. To overcome these limitations, in this paper we embrace the novel peer-to-peer learning scheme for on-device training of home thermal models. Specifically, we adapt the personalized peer-to-peer algorithm proposed in recent work (called P3) to efficiently train personalized thermal models on resource-constrained devices. Our preliminary experiments with data from 1,000 homes, using the LSTM model, demonstrate that the adapted P3 algorithm produces accurate and personalized thermal models while being extremely energy-efficient, consuming respectively 600 and 40 times less energy than the CL and FL schemes. This result suggests that the P3 algorithm offers a privacy-conscious, accurate, and energy-efficient solution for training thermal models for the many homes in the building stock.