It can be shown that for 2d conformal field theories with just two copies of Virasoro symmetry, infinite conserved charges of the Korteweg-de Vries (KdV) hierarchy can be constructed by relating to the quantum sinh-Gordon model. This naturally generalizes the torus partition function / thermal ensemble to a Generalized Gibbs Ensemble (GGE). In the large central charge limit, we will approximate the characters appearing in the GGE and investigate possible transformation properties under generalized modular transformations.