Rigor mortis sets in between 10 min to a couple hours after death, and reaches maximal "stiffness" by 12-24 hours. So based on the limited information you have, he died any time from 10:30 pm to 6:00 am.
If his whole body was stiff by the time you woke up, then death likely was earlier the night before- ( say 1030 pm - 1 or 2 am ) but it would be difficult to know more precisely.
Always ask if you need clarification/more information.
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The term is rigor mortis.
Cooling may inhibit rigor mortis. A warm/ humid room would actually speed onset. If he was fully stiff by the morning, it still means he was dead longer- but it would not help determine any more precisely the time of death.
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The death certificate says: atherosclerotic and hypertensive cardiovascular disease
He was 71 years old
So he had a cardiac event likely a heart attack or a rhythms disturbance that killed him.
This does not change my answer above.
I am sorry for you loss.