We present a tractable stochastic phase model of the temperature sensitivity of a mammalian cold receptor. Using simple linear dependencies of the amplitude, frequency, and bias on temperature, the model reproduces the experimentally observed transitions between bursting, beating, and stochastically phase-locked firing patterns. We analyze the model in the deterministic limit and predict, using a Strutt map, the number of spikes per burst for a given temperature. The inclusion of noise produces a variable number of spikes per burst and also extends the dynamic range of the neuron, both of which are analyzed in terms of the Strutt map. Our analysis can be readily applied to other receptors that display various bursting patterns following temperature changes.