This is fairly simple to do but if your not sure of the electronics be careful ! mains is less forgiving than a battery or low voltage circuits and electrocuting yourself or someone else would be a BAD thing.
Things to consider is using a relay , this will at least isolate the low voltage arduino end from the high voltage, the only problem with this is if its a large load then you can get horrible switching problems.
Solid state relay could be used as an alternative, or then your into switching the mains with a triac and hopefully a zero voltage switch control circuit (i.e. the Triac is only turned on at the start of a voltage phase rise reducing switching currents etc.)
Having said all this I would seriously find someone that nows this stuff and help you direct as a mistake with the mains could seriously harm someone.
All of the arduino's boards would be able to do temperature measurements and control 2 switching circuits easy.