My hypothesis is that it is not possible for heat to be transferred this way because it seems that any matter would simply experience a temperature increase instead of allowing heat to pass through.
Despite this, though, I am uncertain since beta radiation (among other types) seem to be able to pass through solid materials like human skin, for instance.
It depends on the opacity and density of the matter at the wavelength of the radiation.
Examples where energy can pass through, and heat something on the other side: Radio waves passing through walls. Infrared light from the Sun passing through the atmosphere. Light passing through the glass of a greenhouse, heating the inside. Microwave energy in your microwave passing through glass or tupperware. X-ray and gamma rays passing through tissue and other solid matter.
I offer these examples to show you that density of matter, opacity of matter, and wavelength of light are all diverse, leading to diverse behavior.
