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Advances in multi-cores CPUs and in Graphics Processors Units (GPUs) are attracting a lot of attention of the scientific community due to their parallel processing power in conjunction with their low cost. In recent years the resolution of inverse thermal problems (ITP) is gaining increasing importance and attention in simulation-based applied science and engineering. However, the resolutions of these problems are very sensitive to random errors and the computer cost is high. In an attempt to improve the computational performance to solve an ITP, the computational power of multi-core architectures was used and analysed; mainly those offered by the GPU via Compute Unified Device Architecture (CUDA) and multi-cores CPUs via Pthreads. Also, we developed the implementation of the Preconditioned Conjugate Gradient method as a kernel on GPU to solve several sparse linear systems. Our CUDA and Pthreads-based systems are, respectively, two and four times faster than the serial version, while maintaining comparable convergence behaviour.