From a medical website:

April 27, 2011 -- The most common time of day for heart attacks is the morning, and now new research suggests that morning heart attacks are also the most serious. Heart attacks occurring between 6 a.m. and noon were associated with the most the damage in the study, reported Wednesday in the journal Heart.Apr 27, 2011
Risk Factors: Hypertension
Heart Attacks in the Morning Are More Severe - WebMD

From a News website:

Heart attacks are five to six times more likely to occur in the early morning hours between 1 and 5 a.m., and studies have shown that morning heart attacks tend to be more severe than those that happen later in the day.Feb 28, 2012
Heart attacks more common in the morning | Fox News

So people have to decide between the two, 6 AM to noon per the medical site,

Or:

1am-5am per the news site?

Take a pick there are likely a half a dozen other reports claiming this or claiming that, and you will never get a real answer because both answers will no doubt be backed up by serious studies.

People need to not worry so much about stuff, if you are happy being a morning person, then be happy being a morning person. If you enjoy being a night person enjoy being a night person.

Learn you own personal circadian rhythm, and either live with it, or fret over it, because you do not want to live the rhythm you were dealt.