The estimation of heat-related illness cases is a key factor in proposing and implementing suitable intervention strategies and healthcare resource management. This paper proposes new frameworks to estimate the number of patients with heat-related illnesses by administrative wards in Nagoya City using 2014-2019 data. The proposed frameworks are based on the derivation of estimation formulae and machine learning. The daily residual estimation error in the 16 wards was less than one person with both the frameworks. The daily working time average ambient temperature may yield a better correlation than the daily average temperature or daily highest temperature with the number of patients transported by an ambulance from outdoor sites. The results also indicate that patients transported from indoor sites are influenced by earlier ambient conditions over approximately 50 days. In contrast, those transported from outdoor sites are influenced by a relatively short period (20 days), which may correspond to heat adaptation. The frameworks provide a better understanding of the different factors that would lead to an accurate prediction of the number of cases of heat-related patients from weather forecasts. These findings would lead to efficient ambulance allocation as well as public awareness on hot days to suppress heat-related morbidity.