The idea of the analysis is that in polluted water there is an oxygen demand caused by micro-organisms. The required oxygen demand was used to measure the extent if the pollution.
Oxygen demand increases as temperature and time of reaction increases.
See Figure of BOD concentration vs reaction time for various temperatures. Different organics have different oxygen demands per gram of matter and this means that the BOD-analysis only gives an approximate estimate of the weight of oxidized organic matter. TOC is not unambiguously tied to other parameters for organic matter as it states the amount of carbin atoms, but does not say anything about their state of oxidation. Hence, it conveys no information as to how much oxygen should be used for the oxidation.