Hotter or Colder: Find the Treasure
Javascript, 275 279

Not a winner by any means, but this should get things started. Uses a trick with eval() and defining 100 as a "constant" to shave off a few bytes. Ungolfed version below.

function D(){return Math.sqrt((x-n)*(x-n)+(y-m)*(y-m))}
H=100;
n=~~(Math.random()*H);m=~~(Math.random()*H);
P="s=prompt().split(' ')";
eval(P);
x=~~s[0];y=~~s[1];i=0;
while(x!=n||y!=m)
{
    if(i)alert(i&gt;j?"hotter":"colder");
    i=D();
    eval(P);
    x=(x+~~s[0])%H;
    y=(y+~~s[1])%H;
    j=D()
}
alert("correct")


Edit: I fell victim to Javascript's string + number operations, hence why D() wasn't working properly. I also fixed a bug where "hotter" was displayed before "correct". This adds 4 bytes.