Sometimes the best employment you can get is temporary. While they don't offer the stability (or pay) that a full-time job, temp jobs can be very useful for your future career prospects. And, if you play your cards right, you can turn these positions into lasting employment.
Similar to how you can turn an internship into a full-time job, temporary employment can also be converted. It all starts with selling yourself as an employee that can fulfill multiple roles. Hiring managers look favorably upon individuals who are able to show their career skills lie in more than one area. Offer to help with other projects around the office, show you are willing to learn new things. In other words, prove that you are a valuable member of the organization.
It's not exactly easy doing work that you know could end after a specified period of time, especially if the work isn't that stimulating. You still need to try your hardest to keep a positive attitude despite all of this. Sulking around the office will not only hurt your chance of landing a full-time job with the nonprofit, but it will also make the employer less likely to refer you when if you ask for recommendations in the future.
Finally, remember to speak up when you are talking with your temp agency. Tell them you are looking for a job that could eventually turn into steady work. This will allow them to narrow their search for organizations that would be willing to eventually hire you should you do a good enough job.