  We present results, for heavy to moderate quark masses, of a study of
thermodynamic properties of 1-flavour QCD, using the multiboson algorithm.
Finite-size scaling behaviour is studied on lattices of size $8^3\times 4$,
$12^3\times 4$ and $16^3\times 4$. It is shown that, for heavy quarks, the peak
of the Polyakov loop susceptibility grows linearly with the spatial volume,
indicating a first order phase transition. The deconfinement ratio and the
distribution of the norm of the Polyakov loop corroborate this result. For
moderately heavy quarks the first-order transition weakens and becomes a
crossover. We estimate the end point of the first-order phase transition to
occur at a quark mass of about 1.6 GeV.
