In any pulsed and repetitive laser process a part of the absorbed laser energy is thermalized and stays in the material as residual heat. This residual heat is accumulating from pulse to pulse, continuously increasing the temperature, if the time between two pulses does not allow the material to sufficiently cool down. Controlling this so-called heat accumulation is one of the major challenges for materials processing with high average power pulsed lasers and repetitive processing. Heat accumulation caused by subsequent pulses (HAP) on the same spot and heat accumulation caused by subsequent scans (HAS) over the same spot can significantly reduce process quality, e.g., when the temperature increase caused by heat accumulation exceeds the melting temperature. In both cases, HAS and HAP, it is of particular interest to know the limiting number of pulses or scans after which the heat accumulation temperature exceeds a critical temperature and a pause has to be introduced. Approximation formulas for the case, where the duration of the heat input is short compared to the time between two subsequent heat inputs are derived in this paper, providing analytical scaling laws for the heat accumulation as a function of the processing parameters. The validity of these approximations is confirmed for HAP with an example of surface ablation of CrNi-steel and for HAS with multi-scan cutting of carbon fiber reinforced plastics (CFRP), both with a picosecond laser at an average power of up to 1.1 kW. It is shown that for the important case of 1-dimensional heat flow the limiting number of heat inputs decreases with the inverse of the square of the average laser power.