If I have $n$ measured and interdependent time series $M\_1, M\_2, M\_3..., M\_n$ and have $n-1$ forecast time series $P\_1, P\_2, P\_3..., P\_{n-1}$, how can I predict the last forecast time series $P\_n$?

Background: Me and some friends are avid river swimmers and we would like to forecast the water temperature. I have logged the past water temperature along with air temperature, wind conditions and solar radiation for the last couple of years. I also have access to the forecast of all these other parameters.

What I know so far is to filter out seasonality by only operating on the difference from the averages of the historical measurements.

But I lack the the mathematical knowledge to now generate a model which predicts the last time series. Can you give me some indication on what is left to do?

The result is ideally a model which given the past data, current conditions and other parameters forecasts for a given time in the future, gives me the water temperature for this point in the future.