The adjective cordial means being friendly in a formal and polite behavior.
Synonyms are affectionate, cozy, cheerful or jovial.
The word origins from Medieval Latin (14th century) cordialis meaning “of or pertaining to the heart”, “of or for the heart”. It comes from Latin cor meaning “heart” and from kerd– meaning “heart.”
James is always cordial to his father and formal to his sister.
They prepared a cordial welcome to the ministers of these countries.
When she heard of his arrival, she ran very fast and greeted him with a cordial smile.