First, let's learn about the vocabulary to describe how living beings deal with their internal temperature with this answer. Now that you have read this answer, you understand that humans are homeo-endo-therms.

There are pros and cons of homeothermy. Those pros and cons depend upon the species and esp. upon the type of environment experienced by the organism. But broadly speaking, the pros and cons are

Pros

The activity of most chemical reactions are affected by temperature. See this post, this post and this post for examples (this post might also be of interest). Enzyme activities are typically highly dependent upon the temperature.

Homeotherms have the advantage that their internal working is not too affected by the outside temperature allowing them to maintain a high metabolism and a high level of activity in a variety of environmental conditions.

Cons

Depending upon the environment and the species, it may take a lot of energy (and other ressources) to maintain a constant temperature. For example, in mammals we see behaviours such as shivering, hair positioning (piloerection), vasoconstriction, sweating, change in body posture and other systems such as non-shivering heat production by brown adipose tissues.

First, let's learn about the vocabulary to describe how living beings deal with their internal temperature with this answer. Now that you have read this answer, you understand that humans are homeo-endo-therms.

There are pros and cons of homeothermy. Those pros and cons depend upon the species and esp. upon the type of environment experienced by the organism. Here is one pro and one con. In the specialized literature, you;d find a much more exhaustive list of pros and cons

Pro

The activity of most chemical reactions are affected by temperature. See this post, this post and this post for examples (this post might also be of interest). Enzyme activities are typically highly dependent upon the temperature.

Homeotherms have the advantage that their internal working is not too affected by the outside temperature allowing them to maintain a high metabolism and a high level of activity in a variety of environmental conditions.

Con

Depending upon the environment and the species, it may take a lot of energy (and other ressources) to maintain a constant temperature. For example, in mammals we see behaviours such as shivering, hair positioning (piloerection), vasoconstriction, sweating, change in body posture and other systems such as non-shivering heat production by brown adipose tissues.