Lattice field theory is a useful tool for studying strongly interacting theories in condensed matter physics. A prominent example is the unitary Fermi gas: a two-component system of fermions interacting with divergent scattering length. With Monte Carlo methods this system can be studied from first principles. In the presence of an imbalance (unequal number of particles in the two components) a sign problem arises, which makes conventional algorithms inapplicable. I will show how to apply reweighting techniques to generalise the recently developed worm algorithm to the imbalanced case, and present results for the critical temperature and other thermodynamic observables at the critical point, namely the chemical potential, the energy per particle and the contact density. I will also present some preliminary results for these observables at temperatures beyond the critical point.