Automatic Fan Speed Controller

Hello!, I'm new in Arduino and I wanted to make an automatic Fan speed Controller in function of the temperature like this one:

... but the problem is that I have to use 120 Volts instead of 12 Volts. So I wanted to see if this is possible ... I don't want to destroy my Arduino with that high voltage and much less harm myself, so ... that's the reason why I think is a good Idea hear some advices before attempting anything. The same schematic of that webpage works?, What components do I need to change?. At the moment I am not worry about the Code, just the connexions.

If it's an 120V AC fan then it's a much more difficult project: Arduino AC Power Control Tutorial

If the fan has an induction motor or you'll settle for simple on/off control then you should just use a relay. If the fan has multiple speeds then you can use multiple relays to switch between those speeds.

Well... I'm going to explain my project a little better, actually the thing that I want to control is not the fan itself, I want to control the voltage ... I planning to use the same circuit in a resistance that warm something thanks to Joule heating (similar to an iron or a Electric fire). I suppose that is the same principle... I mean, if the temperature increases... then decrease the voltage ... and with that the amperes and warm something a little less ... But if the temperature decreases ... increase the voltage and then the amperes, and of that way warm something a little more. I've already got the resistance, so my problem is the automatic Voltage Regulator, maybe I post the title wrong but the only information that I found in Google of this circuits changing automatically the voltage with the temperature have to be with fans, and I didn't want to confuse because I am not asking about the Joule heating Resistance, I'm asking about the Automatic Voltage Regulator. I'm going to take the 120 Volts from a Socket of my house, I'm not sure if the output should be DC o AC . I hope that is all clear. What can I use?