We report on the experimental investigation of magnetic field generation with a half-loop gold sheet coil driven by long-duration (10 ns) and high-power (0.5 TW) laser pulses. The amplitude of the magnetic field was characterized experimentally using proton deflectometry. The field rises rapidly in the first 1 ns of laser irradiation, and then increases slowly and continuously up to 10 ns during further laser irradiation. The transient dynamics of current shape were investigated with a two-dimensional (2D) numerical simulation that included Ohmic heating of the coil and the resultant change of electrical resistivity determined by the coil material temperature. The numerical simulations show rapid heating at the coil edges by current initially localized at the edges. This current density then diffuses to the central part of the sheet coil in a way that depends both on normal current diffusion as well as temporal changes of the coil resistance induced by the Ohmic heating. The measured temporal evolution of the magnetic field is compared with a model that determines a solution to the coil current and voltage that is consistent with a plasma diode model of the drive region and a 2D simulation of current diffusion and dynamic resistance due to Ohmic heating in the laser coil.