system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: Why is it that when you're cold your body creates goosebumps to essentially warm you up, but when you're sick with the flu and get the shivers your body is already hot?

Why is your body creating goosebumps in a room temperature or even sometimes a hotter environment?
gpt
Part of your body's immune response against infection is to increase the body temperature. White blood cells are more heat resistant than many others, and a lot of the processes that govern viral replication are less stable at higher temperatures, leading to fewer functional viruses being produced. 

In order to increase your body temperature, you only have limited tools. The most straightforward one is for your brain to start treating your surroundings as if they were cooler than they truly are. This in turn causes the homeostatic mechanisms you mention in your question to kick in.

Of course, a lot of your body's normal functions are less effective at higher temperatures as well, so having a particularly high fever, or a fever for a long time, can be bad news.