Think Solid State Relay. Plenty on eBay, and they are a common item in Electronic wholesale/retail places.
I was just looking at one on eBay, complete with heat sink, that will handle up to 380V AC, outputs up to 40 Amps, and is controllable with 5V. It's about 10 bucks, but it's in China. Buy locally for getting it faster. Make sure it has enough capacity (voltage/current), and that it doesn't take too much current to drive it (unlikely to be a big current draw from the Arduino).
That being said, it is NOT something to take lightly, or to be careless around. 220 0r 240V AC can kill you.
You should be able to regulate the temperature very accurately with a PID sketch, as well as timing duration, ramp time for controlled heating or controlled cooldown.