Daily mean temperature is a time series data, and mostly it will be autocorrelated; so you can consider ARIMAX or VAR models to model the relation of daily mean temperature and kidney-related morbidity based on their stochastic characteristics.

Dear Ayman Amin Thank you for your answer. I have an idea about the modeling but I am just looking to understand what is causing autocorrelation in that particular scenario that I stated. Do seasonality and trend cause mean temperature values of one day to another day? and if we adjust seasonality and trend in regression modeling, would there be no correlation in the mean temperature of one day with the other day?

To my way of thinking the auto-correlation in temperature is casual not causal. The mean temperature variations are influenced by the eath's orbit & tilt. The period of that orbit has arbitarily been defined as 1 year by humans. This will cause a virtual autocorrelation of lag 12 months in temperature data. Yet, last December's mean temperature will probably not effect the upcoming December's mean temperature, instead both are being influenced by the same external force.

ARIMA models are rarely "real models", in the sense they are rarely build from first principals or knowledge of the underlying driving forces. Instead they are more like generalized curve fitting functions that can be adapted to most observed time series. ARIMA models are an abstraction & in this sense you should be careful how you interpret them. Most seasaonal models are a heuristic abstraction of reality.

I not sure why you are worried about the autocorrelation in the the independent variable (i.e. temperature). I am not sure where you got that rule that says there can be no autocorrelation in the independent variable in regression fitting. Perhaps you are leaving something out of your explanation.