@CrossRoads
Oh...Great...
Will any amplifier that I find work or do you know of any kind of amplifier that would work best? How would I go about lowering the ADC reference voltage?
"...then freeze it at the temp you think it might to.."
Could you clarify that please? I'm not following that. lol.
I'm sorry. I used the wrong number! Ascent should be about 20 seconds. Yes, it will most likely take a while to come down, though measuring temperatures for that doesn't matter. Yes, I was planning on that. Is that bad? Will that not work? The thermocouples take in one reading for every 0.15 seconds so my team is hoping to get 130 readings.
I was thinking that. I just might do that. Do you think that's the best option? I was also thinking I would probably use micros() too. Awesome!
I was really hoping no one would say that. 
I kinda felt that way too, but it's what the club bought and told me to use and I figured they knew their stuff(This is my first year doing this sort of thing)
How much quicker and easier would this be with one of these IC temp sensor? Would you say they're perfect for use here? Also, how quickly do you think I could get one?
It's completely alright. I had a feeling something like this would come up. lol. So to avoid this messing around with thermocouples you 100 percent recommend IC temp sensors? I'm fine with using them, as long as it saves me time and is easier. I wish I had more time, but our Arduino hasn't even come in yet! I had to take my Arduino off of my Science Fair project and use it for this. lol. Freaking parts. D:
Thanks! I'm going to need it... 