It took me a while to complete the algorithm that extrapolates normals in a triangle. The trick is to compute the area of each triangle defines by the intersection point and the three vertices. Once you get that, just find the weighted mean, and you're done. Here is the code:

float4 v0
= triangle.p0 - intersection;

float4 v1
= triangle.p1 - intersection;

float4 v2
= triangle.p2 - intersection;

float
a0 = 0.5f*vectorLength(crossProduct( v1,v2 ));

float
a1 = 0.5f*vectorLength(crossProduct( v0,v2 ));

float
a2 = 0.5f*vectorLength(crossProduct( v0,v1 ));

normal =
(triangle.n0*a0 + triangle.n1*a1 + triangle.n2*a2)/(a0+a1+a2);

As simple as that :-)