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A new algorithm for digital image processing apparatuses is developed to evaluate profiles of high-intensity DC beams from temperature images of irradiated thin foils. Numerical analyses are performed to examine the reliability of the algorithm. To simulate the temperature images acquired by a thermographic camera, temperature distributions are numerically calculated for 20 MeV proton beams with different parameters. Noise in the temperature images which is added by the camera sensor is also simulated to account for its effect. Using the algorithm, beam profiles are evaluated from the simulated temperature images and compared with exact solutions. We find that niobium is an appropriate material for the thin foil used in the diagnostic system. We also confirm that the algorithm is adaptable over a wide beam current range of 0.11-214 μA, even when employing a general-purpose thermographic camera with rather high noise (ΔT(NETD) ≃ 0.3 K; NETD: noise equivalent temperature difference).