Many protostellar disks show central cavities, rings, or spiral arms likely caused by low-mass stellar or planetary companions, yet few such features are conclusively tied to bodies embedded in the disks. We note that even small features on the disk surface cast shadows, because the starlight grazes the surface. We therefore focus on accurately computing the disk thickness, which depends on its temperature. We present models with temperatures set by the balance between starlight heating and radiative cooling, which are also in vertical hydrostatic equilibrium. The planet has 20, 100, or 1000 M ⊕, ranging from barely enough to perturb the disk significantly, to clearing a deep tidal gap. The hydrostatic balance strikingly alters the appearance of the model disk. The outer walls of the planet-carved gap puff up under starlight heating, throwing a shadow across the disk beyond. The shadow appears in scattered light as a dark ring that could be mistaken for a gap opened by another more distant planet. The surface brightness contrast between outer wall and shadow for the 1000 M⊕ planet is an order of magnitude greater than a model neglecting the temperature disturbances. The shadow is so deep that it largely hides the planet-launched outer arm of the spiral wave. Temperature gradients are such that outer low-mass planets undergoing orbital migration will converge within the shadow. Furthermore, the temperature perturbations affect the shape, size, and contrast of features at millimeter and centimeter wavelengths. Thus radiative heating and cooling are key to the appearance of protostellar disks with embedded planets.