There is no credible evidence that a rapid drop in body temperature after exercise directly causes illness, although improper cooling or exposure to cold conditions post-exercise can contribute to discomfort or other health issues.
You may get sick if your body temperature falls too quickly after exercise.

FactVerify
Source: factverify.com
Key Evidence
Exercise raises body temperature through increased metabolism, and the body naturally cools down afterward via sweating and blood flow adjustments.
polar.compolar.comHow Does Exercise Affect Body Temperature?
livestrong.comlivestrong.comThis Is Why Your Body Temp Goes Up When You Work Out There is no scientific evidence linking rapid post-exercise cooling directly to becoming sick; rather, health risks are more commonly associated with overheating or environmental cold exposure.
hopkinsmedicine.orghopkinsmedicine.orgExercise-Related Heat Exhaustion
What the Evidence Shows
The claim that "You may get sick if your body temperature falls too quickly after exercise" implies a direct causal relationship between a rapid decrease in body temperature post-exercise and becoming ill. Breaking down the claim: 1) Body temperature rises during exercise due to increased metabolic activity and heat production, which is well-documented.polar.compolar.comHow Does Exercise Affect Body Temperature?
livestrong.comlivestrong.comThis Is Why Your Body Temp Goes Up When You Work Out
pmc.ncbi.nlm.nih.govpmc.ncbi.nlm.nih.govControl of Body Temperature during Physical Exercise 2) After exercise, the body cools down through mechanisms such as sweating and increased blood flow to the skin.
This cooling process is natural and necessary for homeostasis. 3) However, none of the reviewed sources provide evidence that a rapid fall in body temperature after exercise directly causes sickness such as infections or systemic illness. Instead, most sources focus on risks related to overheating or heat exhaustion during or immediately after exercise.hopkinsmedicine.orghopkinsmedicine.orgExercise-Related Heat Exhaustion
4) Some sources discuss risks associated with exercising in cold environments, where inadequate protection from cold can lead to hypothermia or cold-related injuries, but this is distinct from the claim about rapid temperature drop causing sickness. 5) The concept of "getting sick" typically refers to infections or immune system responses, which are not directly triggered by changes in core body temperature alone.
While extreme cold exposure can stress the body and potentially weaken immune defenses over time, a quick post-exercise temperature drop itself is not established as a cause of illness. Therefore, the claim overstates the risk and misrepresents physiological processes. It is important to differentiate between normal thermoregulation after exercise and pathological conditions caused by environmental extremes or dehydration.