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We introduce a q-deformation of the genus one sl2 Knizhnik–Zamolodchikov–Bernard heat equation. We show that this equation for the dependence on the moduli of elliptic curves is compatible with the qKZB equations, which give the dependence on the marked points.doi:10.17615/kz5y-hj71 fatcat:zvooifup4nbcjn6lxwak77lnoe