As temporary faculty, how to deal with a colleague who, via email, questions agreements made in a meeting? I'm on a short-term contract with a local state university.  I have been teaching there as an adjunct for a while, but a full-time faculty needed to take emergency leave so I was asked to cover their courses.

As part of my full-time responsibilities, I was asked to a meeting for some administrative work that I know something about.  There were four faculty members: the head of department, a recently tenured faculty, and a tenure-track faculty.  During the meeting we divided up the work and said we'd meet in two weeks or so to review it.

There was some discussion about who did what, but the recently tenured faculty said very little.

The next day, that recently-tenured faculty sent an email saying that they had "felt uncomfortable" with how the work was assigned and had a "clear vision" about the part of the work that I had volunteered for.  As I said, the recently-tenured faculty said very little during the meeting and seemed to agree with the outcome.

In addition to the four people who were at the meeting, this email was CCed to the Dean and the rest of the department.

Coming from a commercial, rather than academic, background I found this behavior disturbing and unprofessional.

My full-time contract ends at the end of the calendar year, but I am wondering if you have any advice regarding how I should deal with this  recently-tenured faculty apart from doing the work that I was asked to do during the meeting?  I'd rather have nothing to do with them and, were they in a commercial environment, they would probably be on a PIP (performance improvement plan).

The head of department has been supportive.  The Dean has not weighed in.
Actually, I would ignore it. It is fairly typical behavior among some faculty. It might not even be abuse, but just the other person having time to reflect after the meeting. If the comments made were on-topic and not a personal attack, then you have nothing to gain in your current position by doing anything beyond arguing for your position. It could even be that the other person is uncomfortable in meeting generally. 

I once found that offering suggestions for improvement of policy, as a new faculty member, is sometimes definitely not appreciated. I suffered setbacks because I suggested that "the way we do things here" was counterproductive. People don't like to hear that from a new person or an underling. 

But yielding graciously, even if you don't feel it, could put you in a better position for future employment there. 

On the other hand, you are justified in responding to a personal attack, but do so through "channels".