Excessive heating of the metal sheet during laser oxygen cutting can cause quality deterioration and even lead to cut loss and possible machine idle time, especially for cutting of thick plates, where the cutting speed is slower. There are at least three different strategies to handle quality deterioration by heat accumulation in flame laser cutting of thick plates: to optimize the process parameters for preheated zones, to generate tool paths that avoid such regions, or to use active cooling to remove the excessive heat. For any of these strategies to work, it is crucial to correctly identify when and where heat accumulations occur. This can be done by real-time temperature measurements, by simulating heat propagation on the metal plate, or by defining empirical criteria based on experimental data. This paper takes a close look at these methods of heat accumulation detection, their advantages and disadvantages, and how they can be integrated into different approaches to tackle unwanted heat accumulations in laser cutting. Furthermore, three case studies are provided, one for each abovementioned method, where the detection of quality degradation due to heat accumulation is demonstrated with a series of experiments. For all case studies, at least one action is proposed to improve the cut quality. All experiments were conducted for 15 mm mild steel plates using a 4 kW industrial fiber laser cutting machine.