The plasma heating by coherent rf fields concentrated in thin layers in a plasma is investigated. This heating method is based on Fermi stochastic acceleration; the transit time acceleration occurs randomly when the rf period is much less than the time between two successive entries of the particle into the localized field. The initial heating rate is provided analytically, and the subsequent variation of the velocity distribution function is followed by numerical calculations. In contrast to previous predictions by Akhiezer and Bakai, it is found that the temperature does not increase in proportion to the square of the time. The temperature exhibits an essentinally linear time dependence.