The weather's warm — fruit tree blossoms will soon bloom.

Literal

Weather [subject-が] warm-[and-て] soon fruit-tree [possessive-の] flowers [subject-が] bloom [probably-だろう].

陽気 here is the noun 'weather / climate' (different from the na-adjective 'cheerful' ). 暖かで is the na-adjective 暖か + で (the te-form of だ), connecting two clauses. やがて ('eventually / soon') is a slightly literary time adverb. 果樹 ('fruit tree') is a formal compound.