When you sleep, your bodily functions slow down and your body temperature drops.
Literal
Sleep [conditional-と] body [possessive-の] function [subject-が] slow become, body-temperature [subject-が] fall.
と as a general conditional — 'whenever X, Y.' Expresses cause-and-effect as a general rule. ゆっくり ('slowly') + になる = 'become slow.' 体温 ('body temperature') + が下がる. Scientific description.