The first thing to do is check with the Jake about the situation. Perhaps there was more to it than was publicly visible, so make sure the situation is what it appears to be first and that the ban (or any other moderator action) was actually unjustified. If it turns out there was more going on and the ban seems justified, explain to Jake how the situation appears at first and coach him on avoiding calling a user names and taking other vengeful actions beyond neutral moderation so that it doesn't appear he is abusing a user in the future.
If, in fact, it is abuse and there isn't more to the situation, then remove the suspension immediately and request that Jake apologize to the user. Mistakes do happen, but moderation comes with added responsibilities to the community and should be held to a higher standard of conduct, so an apology at a minimum is a reasonable expectation. Make sure Jake is aware that he should be mindful of his personal involvement in a situation and seek the aid of another moderator if he becomes too personally involved in a situation.
If Jake is willing to apologize and things can be smoothed over it can probably stop there with Jake being a little wiser to avoid similar situations in the future.
If Jake is unwilling to apologize however, then there is a much bigger problem. If Jake doesn't see why the situation is not ok and demonstrates no willingness to correct for the behavior in the future, either a temporary removal of privileges, a reduction in privileges or a complete loss of privileges may very well be in order. Note that any of these actions are likely to initially cause more drama, but in the long run, having a moderator who has no problem with abusing users and isn't open to being counseled on it is a huge risk to your community.
It is worth playing by ear, but generally, if I see a moderator who clearly has no interest in avoiding abusing their power to get their own personal way in the future, they aren't fit to be a moderator. This attitude goes entirely against the idea behind moderation, where your goal is to be neutral and take the position best for the community rather than best for yourself.