"act warmly" is correct and usable in written English.
You can use this phrase when you want to encourage someone to treat another person with warmth and kindness. For example, you could say, "Let's act warmly towards our guests and make sure they have an enjoyable time."
What a generous heart---the way she acts so warmly with us".
This coolly staged, warmly acted revival brings out the medicinal flavor in Bernard Pomerance's 1979 drama, staged with solemn Brechtian detachment by Sean Mathias.
(The Model T, which is central to the story, appears here, too, but as a 3-D outline of a car.) Warmly acted and agreeably sung, this "Ragtime" travels light.
Currents of longing, thick with hope and hopelessness, eddy through the atmosphere in the warmly acted production that opened last night at the Royale Theater, with a cast led by Jimmy Smits.
And as is made clear by Leigh Silverman's warmly acted new production, which opened last night and runs through Dec. 5, Mr. Shanley had already mapped out the bumpy and bruising road to love that his work has been following ever since.
There is an interesting line of social-science research that suggests cold weather is actually a stimulant to civic energy: people in hot-weather towns tend to disappear from the streets when it's too hot, while in cold-weather towns they get dressed up warmly and act out, stamping their feet and huffing their breath and banging their arms together, doing that whole "I'm cold!" bit.
But by the third act he was in his warmly passionate element.
Their second-act duet, "I Still Get Jealous," is a classic Broadway soft-shoe routine, pristinely staged and warmly performed.
As First Lady, she warmly supported the Iraq Liberation Act of 1998, which made it the policy of the Unites States to overthrow Iraqi President Saddam Hussein.
He was not warmly received, but he did, according to Acts of the Apostles, gain limited (if arguable) concessions.
