Based on the analysis of the effect of temperature on the development of crops, a hypothesis of the mechanism of the effect is advanced. Two quadratic non-linear differential equations are thus constructed. By working out an approximate solution to the differential equations,a new mathematical model showing the relationship between temperature and the development of crops is established. With the new model, a function of temperature, called the effective accumulated temperature variable, is defined. The model is proved to have better results than the old ones in practice.