Some agencies provide health insurance for their longer-term temps.
Morgan Stanley's PAL program has especially good insurance. Ask your agency if they offer insurance, and what the requirements are. Contact your union for details. AGMA also has a program where part of the money your AGMA employer puts in to the union for you gets put aside in a Medical Benefits fund. Periodically, AGMA will send you notice of how much you have in the fund, and you can use this money toward doctors' bills or insurance premiums.