I have a wisdom tooth coming in and I'm getting body chills, face feels hot, neck pain and I've been very tired. Could it be because of my tooth?

Possibly. If that tooth has an associated infection around it, it is possible that it all could be related.
Yes. Infected wisdom teeth can cause the symptoms you describe plus more. If you currently have those symptoms, you need to see an oral surgeon ASAP Antibiotics will be prescribed. The oral surgeon can discuss removal if indicated.