I think your model still falls within the category of Multiple Regression Analysis. Such models can include autoregressive variables as you depict. Translating your model in plain English you have: Energy consumption is a function of Energy consumption in the previous period and the change in temperature.
Depending on how your dependent variable is structured, your model could have a Unit-Root issue. This means that your dependent variable is nonstationary, and is not mean-reverting. In such a case, both the Variance and the Average of (a smaller section of the time series) of the dependent variable can drift in the same direction for too long. If this is the case, your dependent variable is mispecified. And, your model's results are spurious even if the overall R Square is very high and the variables are very statistically significant (this is a very common result with mispecified models).
I think if your variable is Energy consumption for a specific geographical area, you may run into such a Unit-Root situation. As, Energy consumption goes up forever. If your variable is Energy consumption per capita, maybe it is fine as is.
Investigating whether your model has a Unit-Root issue or not, may dictate whether your results are statistically meaningful or not. If it does have a Unit-Root, you need to transform the dependent variable. If you transform it to represent the % change in Energy consumption per capita, you will most probably avoid any Unit-Root issue.