I did a brief literature review:

White blood cells The core cause of the fever starts with white-blood cells (specifically mononuclear phagocytes) that produce endogenous pyrogenic cytokines when they encounter a foreign agent (e.g. bacteria, virus, etc...) that is/produces pyrogen(s) TL;DR: Immune cells release a signal

Through unknown mechanisms they communicate to the brain which increases production of additional factors (likely prostaglandin E2) that then act on thermoregulatory neurons. TL;DR The signal communicates with the brain telling it to allow an increase in temperature (think of it as the brain telling the rest of the body the normal temperature is now 100 degrees).

The major changes are thought to be derived from:

• Neurons expressing PGE2 receptor 3 (EP3) trigger the sympathetic nervous system to trigger norepinephrine release (works with adrenaline as part of your fight or flight response), which elevates body temperature by increasing thermogenesis in brown adipose tissue as well as by inducing vasoconstriction to prevent passive heat loss.
• Acetylcholine contributes to fever by stimulating muscle myocytes to induce shivering.

TL;DR: Mainly the heat is from an increased metabolism in brown adipose tissue

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4786079/ https://pubmed.ncbi.nlm.nih.gov/223485/