In accordance with the Iron Law of Politics that New York City Mayor is a dead-end job, Rudy Giuliani isn't running for the Senate. Remember, all speculation about whether current or former mayors may or may not run for statewide or nationwide office is a total waste of time -- they may run, but they probably won't, and they certainly won't win. We should be free from Bloomberg-for-Anything speculation for a little while after he was almost defeated for re-election, but odds are good that should Obama's approval ratings slip any further, we'll see presidential rumors again. Attend to them at your own peril.
NYC Mayor is a dead-end job, but one can recover from contesting for that office and losing, and then go on to bigger and better things. Therefore, the Iron Laws of Politics have no predictions about whether William Thompson, who lost to Bloomberg this year, will be successful if he seeks higher office.