Thermal convection experiments in a liquid gallium layer subject to a uniform rotation and a uniform vertical magnetic field are carried out as a function of rotation rate and magnetic field strength. Our purpose is to measure heat transfer in a low-Prandtl-number (Pr = 0.023), electrically conducting fluid as a function of the applied temperature difference, rotation rate, applied magnetic field strength and fluid-layer aspect ratio. For Rayleigh–Bénard (non-rotating, non-magnetic) convection we obtain a Nusselt number–Rayleigh number law Nu = 0.129Ra0.272±0.006 over the range 3.0 × 103 < Ra < 1.6 × 104. For non-rotating magnetoconvection, we find that the critical Rayleigh number RaC increases linearly with magnetic energy density, and a heat transfer law of the form Nu ∼ Ra1/2. Coherent thermal oscillations are detected in magnetoconvection at ∼ 1.4RaC. For rotating magnetoconvection, we find that the convective heat transfer is inhibited by rotation, in general agreement with theoretical predictions. At low rotation rates, the critical Rayleigh number increases linearly with magnetic field intensity. At moderate rotation rates, coherent thermal oscillations are detected near the onset of convection. The oscillation frequencies are close to the frequency of rotation, indicating inertially driven, oscillatory convection. In nearly all of our experiments, no well-defined, steady convective regime is found. Instead, we detect unsteady or turbulent convection just after onset.