Let X be a smooth, compact, projective Kähler variety and D be a divisor of a holomorphic form F, and assume that D is smooth up to codimension two. Let ω be a Kähler form on X and $K_{X}$ the corresponding heat kernel which is associated to the Laplacian that acts on the space of smooth functions on X. Using various integral transforms of $K_{X}$, we will construct a meromorphic function in a complex variable s whose special value at s = 0 is the log-norm of F with respect to μ. In the case when X is the quotient of a symmetric space, then the function we construct is a generalization of the so-called elliptic Eisenstein series which has been defined and studied for finite volume Riemann surfaces.