Differentiable structure on the gauge group?

Question

In this paper I have come across a formulation involving differentiation in the gauge group of a principal bundle which I do not understand (found at the very top of p. 369).

Let $P\rightarrow M$ be a principal bundle, $M$ compact (or closed if you require it). Define $g_{t}:[0,T)\rightarrow Gau(P)$, where $Gau(P)$ is the gauge group of $P$. Then the author is able to write $\frac{\partial}{\partial t}g_{t}$, i.e. there is some kind of differentiable structure on $Gau(P)$.

My questions:

1. What is the differentiable structure on $Gau(P)$?

2. What is the tangent space at an element of $Gau(P)$?

My first inclination would be to turn $Gau(P)$ into a Fréchet space, but the only references I could find for this were from 2005 onwards. Since the paper is from a few years earlier, the author might have something else in mind.

Thank you very much.