We investigate the finite time explosion of the stochastic heat equation $\frac{\partial u}{\partial t} = Δu(t,x) + σ(u(t,x))\dot{W}(t,x)$ in the critical setting where $σ$ grows like $σ(u) \approx C(1 + |u|^γ)$ and $γ= \frac{3}{2}$. Mueller previously identified $γ=\frac{3}{2}$ as the critical growth rate for explosion and proved that solutions cannot explode in finite time if $γ< \frac{3}{2}$ and solutions will explode with positive probability if $γ>\frac{3}{2}$. This paper proves that explosion does not occur in the critical $γ=\frac{3}{2}$ setting.