Quenching of hot metal plates during hot rolling, continuous and semi-continuous casting is practised mainly to enhance the material properties of the metal. A large amount of heat is extracted during the cooling process and hence the heat flux should be quantified. In the case of metal with a thickness of more than 5 mm thermal gradients increases in the thickness direction. Therefore, the heat flux on the water impingement region needs to be determined. With the experimental technique, the temperatures are measured on the other side of the impingement region by Infrared thermography. Spatio-temporal temperature data is recorded through Infrared camera at high frame rate of 200 images for every second with a resolution of 640 × 512 pixels. So, the temperature analysis can be done for every 0.5 mm to study the local phenomena. In other words, the cause (heat flux) is predicted from the known effect (temperature). In this work, the finite element method is developed to solve the Fourier partial differential heat equation of the inverse problem. Also, the associated partial differential equations in the adjoint problem and the sensitivity problem are solved using the finite element method. The algorithm used to estimate the unknown heat flux on the water impingement side will be discussed and the results from the inverse problem are validated with the obtained experimental temperatures. The two numerical tests were performed and are discussed.