There are a couple thousand nerve endings per cm² in the finger. The hypothalamus regulates body temperature, but it is the primary somatosensory cortex which receives sensory information from nerve endings such as thermoreceptor. The somatosensory cortex is in the postcentral gyrus which is a ridge located at about mid brain.

1. You should test different rates of temperature change to see how this effects your results. There is an old anecdote about how if you put a frog in a pot of boiling water it will jump out, but if you put a frog in cold water and very slowly heat it, you can cook the frog with out it ever jumping out. I have never heard of this actually being tested (and I do not recommend testing it) but the rate of temperature increase should definitely play a role in your experiment.

2. In order to show that you have a statistically significant result you need to have a sufficient sample size (i.e do many repeats of the same experiment), and you need to have sufficient controls. Try to control for other external variables by testing multiple people. Controlling for the way you administer the experiment by doing it the same each time. Give the people the exact same instructions so you do not biased them, etc.

3. I would not tell them anything about the temperatures. Just tell them that you have three different temperatures and that they need to guess the temperature of exact. This way you would limit the amount to which you bias them by telling which is "hot" "cold" or "medium". Just make sure you use appropriate temperatures so that you do not harm any subjects. Additionally, one thing you may want to consider is the order by which they test the temperature. In other words, do you get different results if they go hot=>warm=>cold vs cold=>warm=>hot or any other order?

Hope this is helpful and good luck with your experiments!