"warmly wish" is a correct and usable phrase in written English.
You can use it when you want to express your sincere best wishes, or when you want to wish someone a pleasant experience. For example: "We warmly wish you a happy and successful new year!".
While I warmly wish success to the plan I would not embarrass my friends by urging it to the prejudice of public objects.
Ringing an old-fashioned school bell to start the show, she would look into the camera, warmly wish a good morning and ask, "How are you today?" She paused so that toddlers at home, watching a somewhat matronly figure in swept-back hair and wearing a wool jacket, could answer.
An acquaintance spots him and greets him warmly: 'Wish you were lunching with us, Johnny!' The two actors meet and sit together.
Waiting to take the stage, he greeted Mr. Pawlenty like the good friend he is, warmly wishing him luck in the debate.
Jim McNally, the Giants' offensive line coach, walked over and shook Stone's hand, clasping his left elbow warmly, wishing him well.
Instead of warmly wishing his sibling all the best, the "Deadpool" star shared a throwback photograph of the pair to Twitter, accompanied by an amusing message.
When I moved on to magazines the following spring, he shook my hand warmly and wished me well.
Smiling warmly, she wished me a nice day and I was on my way.
How? Could that be, how warmly should I wish it.
I wish to warmly welcome the distinguished heads of state and government, the general - the secretary general, the director general of the IAEA, ministers and other distinguished representatives present in the security council chamber.
I wish to warmly thank these audiences.
