Will a non-compete prevent me from working on temp assignments that have been awarded to competitors of my previous employer

No you can't do this. You are aiding a competitor of your company obtain clients that might have gone to your former employer. Live by the agreement, don't get cute with it, and you won't get sued.

I would assume that it would prevent you from taking even temp assignments. The written agreement itself will always prevail and since I don't have that to read, I can't give an opinion with 100% certainty. However, non-compete generally means what it says within a certain territory and under certain parameters. You risk an expensive lawsuit and possible award of damages against you if you try to do an end run by accepting even temporary work. It would be hard to imagine a scenario that would make this worth the risk unless there is some specific exclusion in the non-compete agreement (which is not likely). The second half of your question seems irrelevant. The client relationship with this potential employer is not relevant. The non-compete is with you and governs your conduct, not theirs.

If your non-competition agreement is enforceable, which is impossible to tell without examining it in light of your state's law, then it makes no difference whether you are working in a permanent or temporary capacity. The noncompetition agreement likely prohibits the simple act of competing without distinguishing how you do it. That being said, noncompetition agreements can be invalidated or limited for a host of reasons, including overbreadth in time, territory, or the scope of work prohibitied. If you are concerned about missing this new employment opportunity, you should consult an attorney practicing employment law in your state to advise you as to the enforceability of the non-competition agreement.

You should also keep in mind that, depending on your state's law, the competitor may subject itself to a lawsuit by your prior employer if the competitor knows of your non-competition agreement with your previous employer and nevertheless encourages you to violate that agreement. I, therefore, reiterate that you consult an employment law attorney in your state before proceeding.

DISCLAIMER: I am not your attorney. This answer is not legal advice and does not create an attorney-client relationship.