The influence of nonuniform electric fields on the measurement of the electrical conductivity in pulse-heated wires is studied analytically. Two causes for nonuniformity are considered: switching-on of an external voltage source (transient skin effect) and temperature-dependent change of the electrical conductivity. This problem usually has two strictly different time scales: a short one, on which the transient skin effect takes place, and a long one, on which heat conduction happens. Here, the short time scale is considered.