In framework of a simple microscopic mean-field model for thin smectic-A liquid crystal films with two boundary surfaces the effect of an external magnetic (electric) field on the recently observed phenomenon of layer-thinning transitions in the free-standing smectic-A films upon heating is theoretically investigated. It is found that the external field increases the layer-thinning transition temperatures and decreases the first multilayer jump in the free-standing film thickness. The magnitudes of both magnetic and electric fields necessary for experimental verification of the results obtained are numerically estimated.