We present the results of rf measurements on a niobium-copper clad superconducting radiofrequency cavity with different cooldown conditions and residual magnetic field in a vertical test Dewar in order to explore the effect of thermal current induced magnetic field and its trapping on the performance of the cavity. The residual resistance, extracted from the Q0(T) curves in the temperature range 4.3-1.5 K, showed no dependence on a temperature gradient along the cavity during the cooldown across the critical temperature up to ~50 K/m. The rf losses due to the trapping of residual magnetic field during the cavity cooldown were found to be ~4.3 n/T, comparable to the values measured in bulk niobium cavities. An increase of residual resistance following multiple cavity quenches was observed along with evidence of trapping of magnetic flux generated by thermoelectric currents.