You would start by looking up the Core2 thermal spec. Page 56 shows
how a copper core Intel heatsink is constructed. The copper portion
is circular (presumably, to aid insertion of the copper within
the aluminum portion). This spec also mentions a difference in
thermal resistance, between processors with 2MB cache and 4MB cache,
so in fact there are two different die sizes.
http://download.intel.com/design/processor/designex/31780406.pdf
The die size is listed here as 143 square mm. If the die was
square, that would be 12mm on a side, or roughly half an inch
on each side. But we know it's not square, because for things
like quad cores, they need to put two dice in the same package,
and square die would not be the best for that. In any case,
if the contact point on your heatsink was less than
0.5*1.414 = 0.7" (17mm) in diameter, I'd be a bit worried. If
the copper portion is larger than that, you're OK.
http://www.anandtech.com/show/2045
Using "Core2 143mm" as search terms, I can find this article
http://www.zdnet.com/blog/hardware/inside-the-intel-core-2/45
It has a silicon die shot, but it doesn't say whether that is the
2MB or 4MB L2 cache version. You can take the aspect ratio
of this, and fit the numbers to make 143 square millimeters.
http://cdn-static.zdnet.com/i/story/60/52/000045/core2cpu.jpg
Being none too careful (to avoid scratching my LCD screen),
the die is roughly 4:3 aspect ratio. I didn't measure it
precisely.
Y 4
--- = --- X*Y=143 X*4X/3=143 X=10.3mm Y=13.8
X 3
Diameter-wise, that's a 3-4-5 triangle. Or just doing the
arithmetic SQRT( 10.3^2 + 13.8^2 ) = 17.2mm on the diagonal.
The rectangle should make the diagonal distance a bit longer.
I've checked my math, and my gut says that diagonal value
should be longer, but I've got no tool on this computer for
making scale drawings as a double check. So I improvise.
Using GIMP, I make two images with flood fill, then copy
them to a third image, rotating the square to roughly the
same diagonal as the rectangle. The square is 1200x1200 pixels,
the rectangle 1030x1380 pixels. The diagonal distance is only
slightly different. So 17.2mm diameter heatsink copper
core should cover it

Anything bigger than that,
covers the "spreading angle" of the heat spreader on the
processor lid a little bit, but I doubt that contributed much
to the hot spot. The "thermal image" on the top of the processor,
will be slightly wider, due to the metal lid spreading the
heat a little bit.
http://img141.imageshack.us/img141/7761/gutcheck.gif
Have fun,