  Let $(M,\nabla,g)$ be a Hessian manifold. Then the total space of the tangent
bundle $TM$ can be endowed with a K\"ahler structure $\left(I,{\cal g}\right)$.
We say that a homogeneous Hessian manifold is a Hessian manifold $(M,\nabla,g)$
endowed with a transitive action of a group $G$ preserving $\nabla$ and $g$. If
$(M,\nabla,g)$ is a simply connected homogeneous Hessian manifold for a group
$G$ then we construct an action of the group $G\ltimes_\theta \mathbb{R}^n$ on
$TM=M\times \mathbb{R}^n$ such that $\left(TM,I,g\right)$ is a homogeneous
K\"ahler manifold for the group $G\ltimes_\theta \mathbb{R}^n$. A selfsimilar
Hessian manifold is a Hessian manifold endowed with a homothetic vector field
$\xi$. Let $(M,\nabla,g,\xi)$ be a simply connected selfsimilar Hessian
manifold such that $\xi$ is complete and $G$ be a group of automorphisms of
$(M,\nabla,g,\xi)$ such that $G$ acts transitively on the level line
${g(\xi,\xi)=1}$. Then we construct homogeneous conformally K\"ahler structure
on $TM$.
