The heat kernel is a central object for quantum field theory in Euclidean signature, both for one-loop perturbation theory and non-perturbative functional renormalization group methods. On generic curved backgrounds, however, the link between Euclidean and Lorentzian signature QFT via a Wick rotation is not fully understood. In this talk I will present a proposal for Wick rotating on generic globally hyperbolic manifolds by analytically continuing the lapse function in the ADM decomposition. This keeps the coordinates real and can be shown to define "admissible" complex metrics even under foliation changing diffeomorphisms. A proof of existence of the associated Wick-rotated heat semi-group (and its kernel) will be sketched, and the existence of the strict Lorentzian limit will be discussed.