  We consider the inhomogeneous heat equation on the half-space $\mathbb
R_{+}^{d}$ with Neumann boundary conditions. We prove a space-time Gevrey
regularity of the solution, with a radius of analyticity uniform up to the
boundary of the half-space. We also address the case of homogeneous Robin
boundary conditions. Our results generalize the case of homogeneous Dirichlet
boundary conditions established by Kukavica and Vicol in [10].
