Even if they don't end up being able to offer you a longer term or full time, your employability posture now goes way up on subsequent applications.

(I just had an interview with for a job that will exceed my former salary by thirty percent. Hard, hard unglmaorous work, but hey. .. . And it came through one of those three connections. I reiterate - think hard on people from your past, not bosses, but coworkers for whom you did a good turn or with whom you shared good laughs.)