The phrase "treated warmly" is correct and can be used in written English.
You can use this phrase to indicate that someone was received or responded to with kindness and hospitality, for example: The guests were treated warmly at the dinner party.
More often than not, I am treated warmly.
But W. is going to make sure that the man his father defended through that ugliness gets treated warmly.
Still, we were treated warmly by Mr. Nikolaishvili and his family, who delighted in describing rural customs and teaching us to cook Georgian specialties.
They are treated warmly by everyone, and are perfectly behaved, but then who wouldn't be in an environment where they are, for once, the centre of attention and afforded respect from a group of adults?
The characters are treated warmly and sympathetically, although football pundit Jimmy Hill does end up knocking back the cooking sherry as he struggles to cope with his A-list neighbours (it's never quite clear why he's living among megastars – perhaps he was just a character Cornwell was good at).
They could move to the front of the line for rides and expect to be treated warmly by cast members.
The society added that the people of this pro-Western country feel that Russia-friendly Armenia is treated more warmly than Azerbaijan in the US and UK press.
As an American I found that I was treated more warmly than any time I've visited Europe in the last few years.
We were treated so warmly.
American government and press did not always treat Mandela warmly or nicely.
The kids don't treat him warmly, and when he spews out a vulgar rap during a talent show, the tormenting worsens.
