Final answer:
In determining the time of death, body temperature, signs of stiffness, and body veins bloated with gases provide clues to the postmortem interval. The factor that would not be important in determining time of death is the body having no identifiable cause of death, as this does not influence the timing directly.
Step-by-step explanation:
In determining the time of death for a corpse, investigators must consider several factors related to decomposition and environmental influences. The fact that the body being 32°F and the overall recent temperatures in the area serve as an important piece of information as temperature affects the rate at which a body decomposes. The body being found in a basement and showing signs of stiffness, typically known as rigor mortis, is also a crucial observation, as this is a temporary postmortem condition providing a timeframe for when death likely occurred. Furthermore, the body veins bloated with gases, indicative of the putrefaction stage of decomposition, helps narrow down the window of time since death.
However, the factor that would not be important in determining time of death is 'the body having no identifiable cause of death.' The cause of death generally does not provide direct evidence concerning the timeframe unless it's specifically related to environmental factors that can be linked to a precise time (e.g., a known accident at a certain time). In this case, understanding the cause of death is separate from pinpointing the time of death as it is more about the manner and reason the person died, rather than the postmortem interval estimation.