Learn Russian: Ветер сильный, но ему будет тепло. - The wind is strong, but it will be warm for him.

In Russian, physical states and feelings (like being warm, cold, or sad) are expressed using impersonal sentences. Instead of saying 'he is warm', you say 'to him it is warm'. The person experiencing the feeling takes the Dative case (он becomes ему), and the state is expressed with an adverb (тепло). Because it is in the future, we add the verb будет.

What does будет agree with in the second half of the sentence?

It doesn't agree with anything! Because ему будет тепло is an impersonal sentence, there is no grammatical subject doing an action. In these cases, the verb 'to be' simply defaults to its 3rd-person singular form. For the future tense, that form is always будет.

Why is тепло used here instead of the adjective тёплый?

In impersonal expressions, you must use an adverb (usually ending in -о), not an adjective. Тепло describes the general state or feeling. If you used the adjective тёплый, it would have to attach to a noun to describe its physical temperature, such as тёплый ветер (warm wind).

Why is there no verb in the first part (Ветер сильный), but we need будет in the second part?