While some extra of the Sun’s UV rays slip through the ozone hole, their net effect is to cool the stratosphere more than they warm the troposphere. So this increase in UV rays cannot explain the global warming of the planet's surface.
What scientists have uncovered recently, however, is that the ozone hole has been affecting climate in the Southern Hemisphere. That’s because ozone is also a powerful greenhouse gas, and destroying it has made the stratosphere (the second layer of the atmosphere going upwards) over the Southern Hemisphere colder. The colder stratosphere has resulted in faster winds near the pole, which somewhat surprisingly can have impacts all the way to the equator, affecting tropical circulation and rainfall at lower latitudes. The ozone hole is not causing global warming, but it is affecting atmospheric circulation.