  Graph burning studies how fast a contagion, modeled as a set of fires,
spreads in a graph. The burning process takes place in synchronous, discrete
rounds. In each round, a fire breaks out at a vertex, and the fire spreads to
all vertices that are adjacent to a burning vertex. The burning number of a
graph $G$ is the minimum number of rounds necessary for each vertex of $G$ to
burn. We consider the burning number of the $m \times n$ Cartesian grid graphs,
written $G_{m,n}$.\ For $m = \omega(\sqrt{n})$, the asymptotic value of the
burning number of $G_{m,n}$ was determined, but only the growth rate of the
burning number was investigated in the case $m = O(\sqrt{n})$, which we refer
to as fence graphs. We provide new explicit bounds on the burning number of
fence graphs $G_{c\sqrt{n},n}$, where $c > 0$.
