Modify your History Stats Sensor to record from the start of the day (midnight) to the current time. The today_at() filter reports the start of the day.
- platform: history_stats
name: "High Temperature Hours"
entity_id: binary_sensor.high_temperature_alert_binary
state: "on"
type: time
start: "{{ today_at() }}"
end: "{{ now() }}"
This will now report the number of high temperature hours for the current day. To accumulate this value on a daily/weekly/monthly/yearly basis, use the Utility Meter integration. It stores its data in a separate table in the database that is exempt from purging and meant for long-term storage.
There’s an example here: