According to my findings, the Arduino Uno I linked earlier will fit in the top 5.25" drive bay with room to spare. I considered your other options (and thank you for recommending them), but they were more expensive and I need to stay within budget, hence the cheaper (and bigger) Aruino Uno.
Ohm Resistance Findings
Higher resistance = lower temperature
Lower resistance = higher temperature
Regular room temperature produces the ~10K ohm resistance. Granted the cooking thermometer is not 100% precise and accurate, what is the best way to scale the Resistance values with real temperature values? i.e. is there a standard norm or scalar that is used for these type of 10K ohm sensors?
Hmm... not quite as "standard" as I was hoping (I thought the display might be compatible with the standard Aduino lcd library) but as long as you have a working example to demonstrate how to code for it, that's the important thing. Most of that code seems to be for initialising the display (and should really be in the init function, not loop) and there are ways to simplify that.
Nano 3 and Pro Micro are generally cheaper than Uno. I have purchased Pro Micro for less than £2.50 and Nano 3 for around £3 from China/HK on eBay.
By doing it one thing at a time, getting a short test sketch working for each component. Only then start combining them.
So... list what you have so far. Do you have a breadboard, some resistors, caps, leds and some solid-core hookup wire? What type of Arduino?
If this is your first Arduino circuit, start with the basic flash-an-led sketch first so you know you have the Arduino IDE installed and working and you can upload a sketch.
Then maybe hook up that display and run the test sketch that came with it. The picture of the connectors on the back of the display from the eBay page was blurry. Post an up-close pic. Its an i2c interface, so there should just be 4 connectors: +V, 0V, SCL and SDA. The SCL/SDA connectors must go to specific connectors on the Arduino. Which ones depends on the type of Arduino. You may also need pull-up resistors (usually 4K7) between SCA and +V and SCL and +V.
Have you sucessfully upload anything to the Arduino yet?
Clearly you are going to have to solder some wires to the connectors on the back of the display. Use 4 different colours, ideally red to Vcc, black to Gnd, 2 other colours to sda and scl. Then connect them to +5V, 0V, sda and scl either directly to the Arduino connectors or via your breadboard. Its usual with i2c bus to have a pair of pull-up resistors on sda and scl, but on Uno you can sometimes get away without them.
Then try uploading the sketch you were given for the display. If the sketch uploads ok and nothing happens, try connecting via the breadboard and use your 3K3 as pull-ups.
You cant connect the temp sensors direct to the Arduino because you need to form a voltage divider with a 10K resistor. Have another look at that link you posted earlier to remind yourself.
But concentrate on the display first.
This page tells you which outputs do which jobs on the uno
You will be using the Analog pins for the thermistors, pwm pins for the fans and the i2c bus is referred to as the twi bus on that page.