Your beer will produce the amount/level of carbonation you have decided upon, by calculating the amount of sugar which will give you that. The amount of sugar is calculated taking into consideration the volume of the beer being bottled and the temperature, at which the beer fermented ( highest reading ).
Once the yeast ate all the sugar you added, transforming it into C02, the yeast will no longer do anything. This means, once carbonated, the bottles can be stored at room temperature for months. I would not do that, as you risk losing aroma and flavour ( and probably will ) when exposed to such high temperature, but they can and nothing will happen in termes of bottle bombs? Is that what you are thinking about?
Anyway, once carbonated, the bottles should be moved to a cooler storage room, or directly in the fridge. This will keep the content fresh for longer.