  In rough stochastic PDE theory of Hairer type, rough path lifts with respect
to the space variable of two-parameter continuous Gaussian processes play a
main role. A prominent example of such processes is the solution of the
stochastic heat equation under the periodic condition. The main objective of
this paper is to show that the law of the spatial lift of this process
satisfies a Schilder type large deviation principle on the continuous path
space over a geometric rough path space.
