How would i connect a cpu temp controller to a wall outlet?

Firstly, the temp sensor is on the motherboard, NOT the fan. The unit in the pic is a stand alone temp sensor and most likely gets its power from the pc power supply. Get yourself a cheap furnace thermostat. You'll also need a single pole relay and a voltage source for the relay coil. Make sure the relay coil is low voltage DC, maybe 12 volts so you can use a 12 volt DC power brick. Make sure the relay contacts are rated high enough also. They have to be rated at or above the current consumption the device you are controlling uses for current.

Edit: You haven't clue one about computer wiring in the first place. An IDE cable is a data cable, a 4 pin molex is a power cable. In ANY event, FORGET the computer parts PERIOD. You're going about it bass ackwards.

Edit: ALL your know nothing babble is irrelevant! I AM an Engineer. You ARE wasting your breath and your time. Secondly, what I told you to do IS the most logical approach. Lastly, you have NO business attempting it to begin with. You have about enough electrical experience to put batteries in a flashlight. Are you trying to burn down your house? We are FULLY aware of what all the connectors are and do in a PC. A Molex connector IS a power connector. An IDE connector IS a data pin connector. There are 2 SATA connectors. One is the power connector, the other is the data cable. NONE of these will serve your purpose. END OF STORY.

The unit is a fan controller...it can only "sense" temps from the mother board. IF it has temp senors as a separate wire up you can tape the sensor to whatever you want to check the temp of. The fan is controlled separately and not automatically...unless the controller has that feature. the controller is limited to the Amperage of the fan so only PC fans will work. you have to use a PSU to power that unit. which in turn plugged into the wall socket. The instructions should tell you how to set it up (for a PC only) anything else your on your own!

I'm sure there are units made especially for your application of "home brewing" so you don't have to clobber together some thing that may not work or at least not do what you want it to do. Its just not smart or economical to make Rube Goldberg rig, when you can buy the correct equipment.

It will not do the job. It works at totally incorrect temperatures, and is only designed for very low voltages. Just connecting a charger is likely to be unstable, as chargers are notoriously spiky. Only the batteries they connect to keep them stable. And you have serious issues converting high voltage AC to low voltage DC at the right voltage and current, and stabilised to run the controller. Also a serious risk to heath for someone with no electrical knowledge.