I2C communication between multiple Arduino boards

I am building a resistor network for testing audio amps. I'm using four resistor networks consisting of four 8 ohm resistors each for a total of 16 resistors. I want to use Arduino boards to monitor the temperature of each resistor to control the fans on the heat sink and alert me of any excessive temperatures. I already figured out the thermistor circuit and fan speed control. Can anyone give me an example of programming where a master is collecting data from more than one slave? I want to collect all temp readings on one controller and scroll them on a single I2C controlled display. Will I have a problem with the I2C recognizing the slaves and display from the same master? I also saw a post asking about pull up resistors and I'm not sure where I need them. The simple I2C communication examples didn't use pull up resistors. I will be using Uno boards that I have on hand. Any examples I can experiment with would be appreciated.

Your description is a bit confusing, you state testing amps then it appears it is all on one board. The I2C is not the ideal choice for this, take a look at RS485, CAN, or Wi-Fi. Yes you will have problems with the I2C if the wires approach 1 meter in length. I2C is best used for communicating with components on a circuit board, not inter board communications. If it is on one board a single Arduino will do the task. This response is to help you get started in solving your problem, not solve it for you.
Good Luck & Have Fun!
Gil

Will I have a problem with the I2C recognizing the slaves and display from the same master?

No, as long as you take care to assign different I2C addresses to the slaves.

I also saw a post asking about pull up resistors and I'm not sure where I need them.

An I2C bus always needs pull-up resistors to work. You should take care to have them only once per bus. For simple setups (two Arduinos with short wires in-between) the internal pull-ups (automatically activated by the Wire library) are often sufficient but you'll get problems the longer your bus gets and the more slaves you add (gilshultz already warned you about the bus length, with standard pull-ups the maximum bus length is usually at about 50cm).

Provide links to the four I2C temperature sensors and the display unit you are planning to use with UNO.

My project is built on a single heat sink about 12" square. The resistor networks will be connected to the audio amp under test. I want to monitor the resistor temperatures to control the cooling fans and alert me if they get too hot. I'm using 100k thermistors with 10k SIP9 network resistors to get the temp readings. I can put all the Uno boards right next to each other and use longer leads for the thermistor connections since my temp readings don't need to be exact. My display is a 1602 LCD Display Module connected to a HD44780 IIC/I2C/TWI/SP​​I Serial Interface Port. My issue is I haven't found an example of code that shows how to import the integers for the temp readings. I only have 6 analog inputs per board but I have a total of 16 thermistors to read. There is probably a better Arduino to use with more analog inputs but I have the Uno boards on hand. I don't have a lot of experience with serial communication so I want to give it a shot on this project. The examples I saw on I2C didn't explain it very clearly. Can anyone suggest an example of code I should look at? As Gil suggested I2C may not be the best choice.