The problem of heating a film on a semi-infinite substrate with repetitive high negative bias voltage pulses in contact with a plasma is solved by using the Laplace integral transform technique. The plasma is composed of a collisionless presheath and sheath on an electrically negative film, which partially reflects and secondarily emits ions and electrons. The heating rate of the film attributable to the plasma, the presheath and the sheath, is determined by kinetic analysis. This work proposes a semi-analytical model to calculate the temperature and temperature gradient evolutions inside the film and substrate and provides quantitative results applicable to the control of the temperature evolution. The predicted surface temperature of the film as a function of time is found to agree well with the experimental data. A minimum exits in the temperature gradient profile at a certain depth below the surface. As the heating period progresses, the point of minimum temperature gradient moves towards the solid bulk of the film. The temperature evolution rises periodically and the heat flux evolution oscillates near the vicinity of the surface of the film. In a region beyond a certain depth, the above-mentioned phenomena disappear, and the temperature and temperature gradient evolutions rise monotonically. The effects of the dimensionless pulse duty cycle and the bias voltage on the temperature and temperature gradient profiles could be demonstrated. The temperature at the front surface of the film increases linearly with the pulse parameters. The results show that the temperature and temperature gradient profiles inside the film and substrate are strongly dependent on the pulse parameters.