  Warped conformal field theories (WCFTs) are two-dimensional non-relativistic
systems, with a chiral scaling and shift symmetry. We present a detailed
derivation of the near-extremal limit for their torus partition function. This
limit requires large values of the central charge, and is only consistent for
non-unitary WCFT. We compare our analysis with previous studies of WCFT and its
relation to a one-dimensional warped-Schwarzian theory. We discuss different
ensembles of warped CFTs and contrast our results with analogous limits in
two-dimensional CFTs.
