Heat diffusion within a thermal printhead leads to interactions between printed image pixels over both long and short distances, and results in a sharpness degradation and a distortion of the tone-scale. The loss in image quality is severe, especially if the thermal printhead is efficient and is printing at high speed. We present a novel multi-resolution thermal history control algorithm that delivers a requested print density via a physical model of heat propagation and an empirical model of the media response. The algorithm comprises three recursions, two in scale and one in time. This multi-scale recursive formulation leads to a computationally efficient real-time implementation. Experimental results demonstrate: 1) significantly improved SQF, 2) accurate dynamic and steady-state tone-scale reproduction and 3) equalization of leading, trailing and lateral edge sharpness.