If you can, arrange DifferenceMap to accept a vector of T values. In the ode45() call, instead of passing in the two-element vector [0 T] for scalar T, pass in [0 vector_of_T] . ode45() will report back results at only those times. Discard the first row (corresponding to T = 0) and the rest of the rows hold the results required for each of the values in the vector of T values.
At present, your code is evaluating the same system of ode equations for a number of different T values, but at quite different times -- you do not do T = 1.4 until you have finished all of the T = 1 cases. But in order to simulate to T = 1.4, ode45 would have to integrate starting from scratch, from 0, re-doing the integrations done for time 0 to 1. And then eventually T would become 1.9 and ode45 would have to integrate the same system from scratch again, going all the way through starting from 0 to 1.4 .
My proposal is to do all the times in the same call for a given configuration, so that within the same call after making the prediction for T = 1, it would be able to use the data it already has in order to move on to T = 1.4, and through to T = 1.9 and so on, not needing to re-do the [0 1], [0 1.4] and so on integrations.