"warn you that" is correct and usable in written English.
You can use it whenever you are warning someone about something. For example: "I must warn you that smoking is addictive and dangerous to your health."
According to Austin, one can say 'I argue that' or 'I warn you that' but not 'I convince you that' or 'I alarm you that'.
"Let me warn you, that man [Macron] will destroy our entire social and economic structure," Le Pen told reporters.
I should warn you that the bee is probably going to be at my Friendsgiving.
"ROOM" I should warn you that this film has a very disturbing conceit.
But I must warn you that the punchline cannot be revoked or challenged by anyone.
And I warn you that this is not a perfect description of what the computer does.
I should warn you that I am quoted in the introduction.
"I warn you that insulting people would only intensify their rage".
The on-screen prompts will warn you that all your data will be lost.
This is to warn you that we've got our eyes peeled for you lot, chummies.
Andy Sernovitz reveals the biggest clue that will warn you that a conference is going to be awful.
