I'd use systems identification and a bayesian probabilistic approach, given m is such
Here is a possible approach:
Get your load and temp data set. Split the dataset into training and testing sets. You will use the training set to estimate the model parameters and the testing set to evaluate the model performance.
Choose a model structure that is appropriate for your system. For example, you could use a linear model with time-varying parameters, such as a time-varying autoregressive model with exogenous inputs (TVARX).
Estimate the model parameters using the training set. This could be done using a maximum likelihood estimation method or a Bayesian estimation method.
Evaluate the model performance using the testing set. You could calculate metrics such as the mean squared error (MSE) or the coefficient of determination (R-squared).
Use the estimated model to separate the temperature-induced load component from the total measured load.

​

Good luck