Although some object to any use of awful or awfully in any sense not connected with a feeling of awe, both have been used in other senses for several centuries. Awful and awfully as adverbial intensifiers—awful(ly)hot; awful(ly)cold—appear in the early 19th century, following much the same pattern as horribly anddreadfully. As an adverb awful is less formal in tone than awfully. In the sense “inspiring awe or fear” awesome has largely replaced awful.
c.1300, agheful "worthy of respect or fear," from aghe, an earlier form of awe (n.), + -ful. Replaced Old English egefull. Weakened sense "very bad" is from 1809; weakened sense of "exceedingly" is by 1818.