Understanding the role of the $\theta$ parameter in QCD and its connection with the strong CP problem and axion physics is one of the
major challenges for high energy theorists. Due to the sign problem,
at present only the QCD topological susceptibility at low temperatures is well known. Using an algorithmic approach that could potentially be
extended to QCD, we study as a first step the $\theta$-dependence in
the massive Schwinger model, and try to verify a conjecture of Coleman.