The crossword solutions for the term 'quite cordial' are 'WARM, ' which is a four-letter word. The term 'quite cordial' is an expression used to describe a friendly and polite attitude. It implies that the person is more than just polite, but also genuinely friendly and welcoming. The word 'WARM' is often used to describe a feeling of comfort and hospitality, which is what 'quite cordial' is meant to convey.