Learn Russian: День жаркий.

Nouns ending in a soft sign (ь) can be either masculine or feminine, so you often have to memorize them. День is a masculine noun. Because of this, any adjective describing it, like жаркий, must also be in the masculine form.

Why does the masculine adjective жаркий end in -ий instead of the standard -ый?

This happens because of a very important Russian spelling rule. You can never write the letter ы after the letters к, г, х, ж, ч, ш, or щ. The base of the word ends in к (жарк-), so we must use и instead of ы, giving us the ending -ий.

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

In Russian, the present tense of the verb 'to be' (am, is, are) is almost always left out. To say 'The day is hot', you literally just say 'Day hot' (День жаркий).

If жаркий is an adjective, couldn't this phrase also mean 'a hot day'?

Yes! Because Russian doesn't use words for 'a' or 'the', and drops the word 'is', the exact same words (День жаркий) can mean 'a hot day' or 'The day is hot'. You will easily know which one it is based on the context of the conversation.