An analytical asymptotic expression of the response function χ for fast non-relativistic electrons of a magnetized plasma, accounting for the lowest order corrections introduced by a finite temperature of the bulk electrons, is deduced as a solution of a Spitzer problem. Toroidal effects are included by means of the square well approximation model for the magnetic field. It is shown that the absolute value of χ increases compared to the case where no finite bulk temperature is considered. The effects on current drive efficiency are also discussed.