Here is the 1-d heat equation using Green's functions in radial coordinates:
http://greensfunction.unl.edu/glibcontent/node12.html
An easier method would be to use a Heisler Chart:
http://en.wikipedia.org/wiki/Heisler_Chart#Sphere
There is a link on the wiki page for Heisler Charts to a freeware program that solves simple heat problems here:
http://faculty.virginia.edu/ribando/...OneDTransient/
Neato!