We propose an approximation that makes the price dynamics of heating degree day (HDD) and cooling degree day (CDD) temperature futures linearly dependent on the underlying temperature. The approximation is analyzed both theoretically and empirically. We base our analysis on a continuous-time autoregressive stochastic dynamics for the time evolution of temperature in a given location. The model is fitted to temperature data collected in New York over a long time period. We apply our results to derive a simple version of the Black-76 formula for pricing a call option on CDD and HDD futures.