Patients who are bedridden for a long time are afflicted with multiple problems. Inactive and bedridden patients under sustained pressure are prone to pressure ulcers. High skin temperature and humidity also induce pressure sores. Thus, using automated assistance to measure contact temperature and humidity is a viable solution. A low-cost monitoring device is desperately needed by institutes to improve the quality of care. We embed a few thermostats inside a mattress and estimate the temperature distribution of the entire body on the contact surface of the mattress. The heat flux and temperature distribution, as well as necessary thermal parameters, can be reversely estimated from the measured temperature trajectories of the embedded thermostats by using heat diffusion equations in the finite difference method and the dual iterative estimation of an unscented Kalman filter. We conduct 1D and 2D experiments in a controlled environment and obtain excellent results. The estimated temperature map and heat flux are accurate for a constant amount of flux. Our algorithm is proven to be pragmatic because our findings show that measurements can be taken without knowing any dimensions or thermal properties of the mattress. This will help to prevent bedridden residents from developing pressure sores.