Recognize that temp work can lead to a permanent position if that's your ultimate goal. Temp work has great appeal to workers (freedom to choose assignments, exposure to more employers, and the possibility of better pay) and employers (the availability of top talent when needed). Embrace the idea of being a temp, freelancer, independent contractor.
Temp work can be a paid audition, allowing you to get your foot in the door at a great organization. It's also a way to wow a staffing firm to send you out for more and better assignments. And it offers current experience for your resume which can ultimately lead to a full-time role elsewhere.
In addition to staffing firms, pursue temp work through direct employers as well. (Employers hire even more temp workers directly than through staffing firms.) Use keywords "temp," "part-time" and "contract" to generate results in your online search inquiries.