Integrate over time and differentiate to get slope

Hi All,

I have a set of data with the following channels: Oil Tank temp (T1), Oil Cooler Out Temperature(T2), Pump Speed and Pump Torque. For simplicity I've included a diagram as I cannot include the data.

The pump cycles on and off for set periods, something like the graph below. We do not measure flow rate.

In the data there appears to be a time constant (i.e there isn't a strong correlation between T2 and T1 but if we compare over different periods of time there might be). I have been told to integrate speed / load over different time periods (10, 20 30 secs etc.) and then differentiate to get the slope.

In this case we have both T1 and T2 in the future we will only have T1 so would like to be able to predict T2.

How would one go about doing this in MATLAB?