Learn French: Sa tête est chaude, il est malade.

Yes! In French, possessives like 'his' or 'her' match the gender of the object being owned, not the owner. Because tête (head) is a feminine noun, we use sa tête, even though the head belongs to a man.

Why does chaude have an 'e' at the end?

Because it is describing tête, which is a feminine noun. The masculine form is chaud (where the 'd' is silent). By adding the 'e' for the feminine form chaude, we also change the pronunciation so that the 'd' sound is clearly spoken.

I learned to use the verb avoir (to have) for being hot. Why does this use est (is)?

When a person feels hot overall, French uses avoir: Il a chaud (He feels hot). But when a specific physical object or body part is literally hot to the touch, you use être (to be) and treat it like a normal adjective: Sa tête est chaude (His head is hot).

How can I use the new phrase parce que (because) to connect these two thoughts?

You can use parce que to join these two separate sentences and explain the reason for his illness. You just put it between the two facts: Il est malade parce que sa tête est chaude (He is ill because his head is hot).