The paper considers the problem of finding a lower bound for the Dirichlet heat kernel \(K_D(t,x,y)\) of the semigroup \(\exp[t\Delta_D/2]\), where \(\Delta_D\) is the Dirichlet Laplacian of a proper, open and connected domain \(D\subset\mathbb{R}^n\). The author improves under some geometrical assumption some results of a lower bound for \(K_D(t,x,y)\), \textit{M. van den Berg} in [J. Funct. Anal. 88, 267-278 (1990; Zbl 0705.35052)]. The lower bound here is expressed in terms of \(\theta_4(0,q)\) -- the fourth Jacobi theta-null function and contains the product \(d(x) d(y)\), where \(d(x)\) is the distance function from the boundary of \(D\). (Theorem 3.1), differing from van den Berg estimate where the expression \(d(x)\wedge d(y)\) appears.