Baby temperature after vaccination?

Can be elevated. Vaccination like the illness it's designed to prevent (or reduce in severity) may cause fever as a normal physiologic response. In the animal kingdom, fever helps fight infection. Consider experiments where cold blooded animals given a bacteremia survive better when exposed to heat as opposed to their normal cold, damp environment.
Not often. Today's vaccines are not as likely to cause a fever as the ones back in the 70s. There is always a small chance that within the first 24 hours a fever may show up. Recent studies have shown it is best not to use Tylenol (acetaminophen) if the child is not hurting. Fever is sign immunity is working and blocking it can cause the vaccine to be less effective.