I think you are a
Cloud
Title: Don't Look For the Answer Locally
Computer data can be stored locally or in "the cloud".
Behold! Within a half-digested mess
Digest is a synonym for understand. A "half-digested mess" could mean something poorly understood, which could also be described as cloudy.
A floating, changing form of loveliness.
Clouds float in the atmosphere and come in many forms. Their shapes (which appear fluffy and soft) also change over time because they are made of gaseous vapor. Or, this refers to the phrase "on cloud nine", which means that something is pleasant.
A scale of heat and oh, so deafening-
C (celsius or centigrade) + LOUD (deafening). CLOUD.
No wonder it can be bewildering.
Cloudy can mean confusing and unclear, which are synonyms for bewildering.
Beneath it all is gloom and misery
Cloudy skies is a metaphor for sadness and/or darkness.
But fortified it stands ideally.
Possibly refers to how solidified water vapor is ice, which is solid and hard. According to the comments, it refers to the song Castle on a Cloud.