We address the problem of image color quantization using a Maximum Entropy based approach. Focusing on pixel mapping we argue that adding thermal noise to the system yields better visual impressions than that obtained from a simple energy minimization. To quantify this observation, we introduce the coarse-grained quantization error, and seek the optimal temperature which minimizes this new observable. By comparing images with different structural properties, we show that the optimal temperature is a good proxy for complexity at different scales. Noting that the convoluted error is a key observable, we directly minimize it using a Monte Carlo algorithm to generate a new series of quantized images. Adopting an original approach based on the informativity of finite size samples, we are able to determine the optimal convolution parameter leading to the best visuals. Finally, we test the robustness of our method against changes in image type, color palette and convolution kernel.