Are extremal 2D black holes really frozen?

In the standard methodology for evaluating the Hawking radiation emanating from a black hole, the background geometry is fixed. Trying to be more realistic we consider a dynamical geometry for a two-dimensional charged black hole and we evaluate the Hawking radiation as a tunneling process. This modification to the geometry gives rise to a nonthermal part in the radiation spectrum. We explore the consequences of this new term for the extremal case.