The body will lose a degree or two of internal temperature per hour after death. Rigor Mortis (stiffening of the body) sets in within a few hours (as early as a couple of hours after death, as long as six). If the body was not yet stiff, you can be fairly certain your friend's father died within a few hours of your arrival. But if he was already cool to the touch, it is certainly possible that he died earlier than the nursing home claims.
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