This paper is concerned with the problem of symmetry of domains related to parabolic overdetermined problems. Given a non-constant function satisfying \[ (\Delta-\partial_t)u=-\delta_0 \text{ in }\Omega\quad{\text{and} } \quad u=0 \text{ on } \partial_{\text{par}}\Omega, \] the author presents some conditions that \(\partial_{n_x}u\) satisfies on \( \partial_{\text{par}}\Omega\setminus \{t=0\}\), which guarantees the domain \(\Omega\) is, in fact, a heat ball.