Fly traveling a through a point, along curve of intersection

Question

The temperature in 3-space is given by:

$$ T(x,y,z)= \frac12(2x^2+5y^2+4z^2) $$

At time $$t = 0,$$ a fly passes through the point $$(\sqrt{15},\sqrt{10},5),$$ flying along the curve of intersection of the surfaces

$$ z = x^2-y^2 $$ and $$ z^2 = x^2+y^2 $$

If the fly's speed is $2$, what rate of temperature change does it experience at $t=0$?

So far, I've tried:

1. Finding the normals for the surfaces
2. Finding a tangent vector to the intersection in the point given
3. Finding the fly's velocity vector, v
4. $$ v*\nabla T(\sqrt{15},\sqrt{10},5)$$ Picture of my quick calculations (excuse the handwriting)

Thank you for any help.

Edit: To clarify: The work I've done gave me an incorrect answer; so I'm looking for any input on what I've done wrong and/or what the correct answer to my problem would be. Cheers!