At stock speeds your temp will be similar to a quad at the same speed. As for cooler. You will be fine at stock speeds with the stock cooler. Any higher and i would recommend a new cooler
Yes of course there will be more heat, you just activated two cores! If you have CnQ enabled then idle temps could be only 1C or 2C higher, but at load yes big difference.
Yeah you're going to want to pickup an aftermarket cooler OP. My default is always the Freezer 7 or Freezer 64 pro from Arctic Cooling. It can usually be found for $20 and has a 90mm fan which moves a good deal of air. For the price, its an excellent unit.
If you really want to push your chip or its surrounding components as high as they'll go you're going to want something that's 120mm big, and that stuffs all $50+ I'm afraid.
The Kingwin XT-1264 is another good and cheap alternative. It is very similar to the Cooler Master 212+ but cannot accommodate a second fan. Got mine for $24 shipped from mwave.