Temporary labor is sometimes dismissed as not having any upward mobility. This isn't necessarily true. Many temporary laborers find an exceptional fit where they can excel. In these cases, a business will very often keep someone around by hiring them full-time. Are there ways that you can increase the chances of this in your temporary position? Absolutely. First and foremost, make sure you're working with a skilled staffing company.
A quality staffing agency won't just look at your resume and stick you in whatever job comes along. They'll get a feel for where your strengths lie and what you want. They'll also have a feel for what personalities mesh with different businesses' cultures.
This is key. Temporary labor that's hired full-time usually gets along well with an employer naturally, and a skilled staffing company will find the best fits for you in terms of your talents and your working personality.
The most basic way to get hired full-time is to excel at your work. If you can be more productive, there'll be a strong motive to keep you.
Disinterest is one of the first things that can get a contract terminated. Be interested in what's happening on the job around you. Talk to people and listen to what they say. To think you're a good fit to join a team permanently, someone has to think you're interested in doing so.
Now this is a double-edged sword. If you socialize too much on the job, you won't get any work done. At the same time, don't just hole off in a corner counting the hours go by. If you're isolated, it won't seem like a good fit. This can be hard for some, but a little extra push to socialize can go a long way in co-workers liking you and wanting you to be hired on.
Act the Part
Show up on time. Maintain your self-motivation. Let the little, everyday complaints slide by. Act like you want a full-time position and as if you already have it, and it will be easier for others to imagine you filling it.