Learn Arabic (Modern Standard): الشهر الرابع حار.

In Arabic, ordinal numbers (like first, second, third, fourth) act exactly like adjectives. Because adjectives always come after the noun they describe, we literally say "the month the fourth" (الشهر الرابع).

Why does الرابع (fourth) have ال (al-) attached to the beginning of it?

Since ordinal numbers act like adjectives, they have to match their noun. Because الشهر (the month) has ال (al-) to make it specific, الرابع must also have ال to match it.

Where is the word for "is" in this sentence?

Arabic doesn't use a word for "is" in simple present-tense sentences. You just put the subject (الشهر الرابع, the fourth month) right next to the information about it (حار, hot), and the "is" is naturally understood.

Why doesn't حار (hot) also have ال (al-) at the beginning to match?

If we added ال to حار, it would just be another matching adjective. The phrase الشهر الرابع الحار would mean "the hot fourth month" as an incomplete thought. By leaving ال off, حار becomes the news or conclusion of the sentence, giving us "The fourth month is hot."