The thermal perceptron is a simple extension to Rosenblatt's perceptron learning rule for training individual linear threshold units. It finds stable weights for nonseparable problems as well as separable ones. Experiments indicate that if a good initial setting for a temperature parameter, T0, has been found, then the thermal perceptron outperforms the Pocket algorithm and methods based on gradient descent. The learning rule stabilizes the weights (learns) over a fixed training period. For separable problems it finds separating weights much more quickly than the usual rules.