I wonder what the temperature will be like tomorrow.
Literal
Tomorrow [possessive-の] temperature [topic-は] how probably [question-か].
どうだろうか is the casual self-directed 'I wonder how/what' — だろう hedges the conjecture, か makes it a question to oneself. Common in internal monologue or musing aloud. More natural than 'what will X be?' as a direct question.