換気, 冷房, and 暖房: Ventilation, cooling, and heating
Compare ventilation with the state, settings, and use of cooling and heating. Read a temperature-setting adjustment as an action with a stated purpose, without assuming the bill fell.
換気 as ventilation
換気（かんき） means ventilation. In 「窓を開けて部屋を十分に換気した。」, the speaker opened the windows and thoroughly ventilated the room. Opening the windows and ventilating the room are both described.
In 「料理中は換気扇を回して換気する。」, ventilation takes place by running the exhaust fan during cooking. The English translation, “While cooking, run the exhaust fan to ventilate the room.”, expresses this as an instruction.
The state and settings of 冷房
冷房（れいぼう） means air conditioning or cooling. In 「冷房が効きすぎているので、上着を羽織りました。」, the air conditioning was too strong, so the speaker put on a jacket. That state explains the clothing choice.
In 「電気代を抑えるため、冷房の設定温度を見直した。」, the air-conditioning temperature setting was adjusted to reduce the electricity bill. 抑えるため states the purpose of that adjustment; the sentence does not report that the bill actually fell.
Using and stopping 暖房
暖房（だんぼう） means heating. In 「寒かったので部屋の暖房をつけました。」, the speaker turned on the room's heating because it was cold. The cold is the reason for turning it on.
In 「春になり、学校では暖房を使わなくなった。」, the school stopped using the heating when spring came. 換気 describes ventilation, while these 冷房 and 暖房 examples describe conditions, settings, and use of cooling or heating.
Does 電気代を抑えるため、冷房の設定温度を見直した say that the electricity bill actually fell?
Show the answer and why
It says the setting was adjusted with the purpose of reducing the bill. The purpose expressed by ため is distinct from a confirmed reduction in the bill.