Choosing the right model for prediction

In lieu of an absolute or a priori answer, you could use your existing temperature data to evaluate the performance of the different prediction methods.

E.g. say you have 30 days of temperature data. Perform a set of trials, for both models, where you train the model on some initial segment of the data, say, days 1..n, where n<28, and record the prediction of the model for day n+2. This will give you some empirical evidence of the performance of the different models, given your data.

If you need more temperature data, you could always use a massive dataset like Berkeley Earth.