Hello, John. Actually, no. They are not synonyms. They have two very different meanings. "Pronto" means "soon", "temprano" means "early". Some examples of sentences might leave this clear.
Ella llegó temprano ayer.
Yesterday she arrived early to work.
This does not mean that she did it "soon". She may have taken three hours to get to work, but she still did it early.
Puedo ir pronto a verte ¿está bien a las 23:00?
I can come see you soon. 23:00 is ok?
As you can see, "pronto" (soon) means "in a short time", but it does not imply that is it "early".
I hope this helps.