  We give a brief introduction on finite temperature phase transitions in
lattice QCD including a discussion on the identification of first order
transitions. We present a study of the deconfinement phase transition of
one-flavour QCD, using the multiboson algorithm on lattice of sizes $8^3$,
$12^3$ and $16^3\times 4$. For heavy quarks our results are characteristic of a
first order phase transition which gets weaker as the quark mass decreases and
ends at a critical value of $\kappa \sim 0.1$ or in physical units at about 1.6
GeV.
