Exact solution of heat conduction equation

Hi all,
I am trying to find the exact solution of the 3D heat conduction equation.
The problem I have is I have infinite large 3D body. Then the initial condition is : in the center it is a constant temperture T1; all the other places have temperature T2. The boundary condition is the center point has a constant temperature T1. Does anyone know the analytical solution for this problem?

I checked some material. It seems it has the form:

T(x,t) = 1/sqrt(4*pi*α*t)^(2/3) * exp(-(x^2+y^2+z^2)/4αt).

But it seems it does not include T1 and T2.

Thanks in advance.

Best

Xu