  In this paper, we study the heat kernel associated to the intrinsic
sublaplacian on a quaternionic contact manifold considered as a subriemannian
manifold. More precisely, we explicitly compute the first two coefficients
$c_0$ and $c_1$ appearing in the small time asymptotics expansion of the heat
kernel on the diagonal. We show that the second coefficient $c_1$ depends
linearly on the qc scalar curvature $\kappa$. Finally we apply our results to
compact qc-Einstein manifolds and prove the spectral invariance of geometric
quantities in the subriemannian setting.
