Why does exhaustion sometimes cause fever?
Exhaustion (if you mean being extremely tired due to strenuous exertion) would cause a temporary fever due to the exertion/caloric expenditure/heat, particularly if one was not sweating sufficiently to maintain a near-normal body temperature. Or if the weather was particularly warm and/or humid. Example: heat exhaustion or heat “stroke” in a marathon runner during a hot & humid summer race who did not adequately hyrdrate themself.