Warped conformal field theories (WCFTs) are a novel class of
non-relativistic theories. A simple, yet non-trivial, example of such
theory is a massive Weyl fermion in (1+1)-dimensions, which we study in
detail. We derive general properties of the spectrum and modular properties
of partition functions of WCFTs. The periodic (Ramond) sector of this
fermionic system is non-trivial, and we build two novel partition functions
for this sector which have no counterpart in a two dimensional CFT. The
thermodynamical properties of WCFTs are revisited in the canonical and
micro-canonical ensemble.