I have a time series of daily temperature with autocorrelation that looks like this: Of course, temperature is heavily autocorrelated. When looking at the partial autocorrelation plot, lags are significant up to the 15th lag. But now I want to use this data as input for a regression model of a dependent variable y (perhaps something like heating), and I am wondering how many lagged values of temperature I should add. $\text{heating}=c+\beta_0T_{today}+\beta_1T_{yesterday}+...$ Should I add all fifteen of them? It seems a little much. Especially since I don't think the temperature of fifteen days ago will influence the amount of heating done today very much.

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