Was closing the air conditioner and then opening it in response to the father's anger and his not waking up for Fajr prayer, fearing that he would be obstinate and intentionally abandon prayer, truly the right thing to do?

You will be rewarded for your eagerness to wake your father for Fajr prayer. However, it is not permissible to do anything that displeases him, such as turning off the air conditioner while he is asleep, as this is an act of wrongdoing. Ibn Muflih mentioned in Al-Adab Al-Shari'ah that Ahmad stated it is not permissible for a son to mistreat his parents, even when enjoining good upon them or forbidding evil from them. Rather, he should teach them with gentleness and leniency, without violence or harshness in speech. Therefore, strive to advise your father and urge him to pray on time with gentleness and leniency.