How to give a heads up to people from a different company that the CEO of the company I work for has anger issues?

Say I am a supplier, come to your company, and you tell me “be careful around our CEO, he might threaten to punch you, and if he threatens you, he means it.”

There’s a good chance that you lose your job. Because I’m not going to your company, I will tell my manager, it will reach my CEO who will talk to your CEO, and your job is gone.

It’s better for you if you see what happens, and when he goes to court for assault you can be a witness if you like.

I'm going take a different approach to the other answers.

First of all, whether you give a heads up to people outside your company or not, the problem still exists, and that problem is the CEO creating a hostile work environment, and his actions should be treated as such.

Thus the correct course of action is to report your CEO to HR.

While there is the "saying HR is not your friend", there is the other side of that coin which is that HR is there to protect the interests of the company. And right now the CEO's actions are huge risk factors for the company. These factors could influence outside vendors to not do business with you, but IMHO what is worse for your company is that the CEO is opening up the potential of a lawsuit against the company from a (future) former employee. And this is the sort of thing that HR is meant to head off.

You should not.

Other people who interact with your CEO should not be expected to have to walk on eggshells to coddle your CEO simply because his temper issues. Don't transfer the problem.

It's entirely reasonable to expect your CEO to act professionally and restrain himself.

Bad results come from the acts of someone with the best intentions. Refrain from even raising the topic with anyone, any other company, and don't make any attempt to give some advice before someone meets your CEO. He will bury himself.

If he has directed rage towards you, handle it professionally by staying calm, walking away and reproach, but most importantly, contact HR.

If employees come to you with complaints about him, listen to their whole story, take notes, and advice them to speak with HR and you should hand HR your notes. If there is a Hotline Number posted in your company, encourage anyone who approaches you about your CEO that wants to remain anonymous, call the number, file a complaint, and reassure them that they won't experience any retaliation from coming forward.

Most importantly, be your employees' support through this issue. Sounds like its a bad one.

As an IT Analyst, I don't really see this as your responsibility. Its rare that anyone outside the company, who would work with you, would also want to talk to the CEO. You should just insulate the CEO from the outside world within your realm.

Now you may use a site like GlassDoor for any potential employees and post anonymous reviews of the company, but that may backfire while you work for them. Once you leave, sure.