We consider  semilinear parabolic equations of the form
\begin{equation}
  \label{eqabst}\tag{A}
  u_t=u_{xx}+f(u),\quad x\in \mathbb R,t\in I,
\end{equation}
where   $I=(0,\infty)$ or $I=(-\infty,\infty)$.  Solutions defined for all  $(x,t)\in\mathbb R^2$ are referred to as entire solutions. Assuming that  $f\in C^1(\mathbb R)$  is of a bistable type with stable constant steady states $0$ and $\gamma>0$, we show the existence of an entire solution $U(x,t)$ of the following form. For $t \approx -\infty$, $U(\cdot,t)$  has two humps, or, pulses, one near $\infty$, the other near $-\infty$.  As $t$ increases, the humps move toward the origin $x=0$, eventually  ``colliding''  and forming a one-hump final shape of the solution. With respect to the locally uniform convergence, the solution $U(\cdot,t)$ is a heteroclinic orbit connecting the (stable) steady state $0$ to the (unstable) ground state of the equation $u_{xx}+f(u)=0$. We find the solution $U$ as the limit of a sequence of threshold solutions of the Cauchy problem for equation (A).