Nope, not possible.
What? But I still get warm under glass.
Right, you do still get warm under glass. What happens is that the radiation from the sun gets absorbed by the glass. How does that work?
Well, glass is made up of atoms. And inside these atoms, electrons are living in different quantized energy levels. Think of it as shelves of electrons at different heights. The quantized parts means that electrons can exist only in those shelves, and no where in-between, where there are no shelves. Electrons, however, can move to different energy levels, shelves, through excitation, when it absorbs enough energy. In a metal, a conductor, the shelves are very close together that they appear continuos. In this case, there is always an existing shelf for the electron to reside in when it is excited. However in an insulator, like glass, the shelves are separated by a gap and in order for the electron to move from one shelf to another, a certain amount of energy must be applied to the electron. Energies too little will not be enough to excite the electron to the next energy shelf, and energies too large will excite the electron to a nonexistent shelf. What the electron does in those two cases is nothing, it refuses to accept the energy given to it, because it cannot exist in a non-existing energy shelf. So in the case of sunlight, when the light and radiation from the sun comes into contact with the glass, the energy in the light part of sunlight is not enough to excite the electrons in the glass atoms to a new energy level, and therefore just goes straight through the glass, warming you. The radiation part, however, just so happens to be the perfect energy needed to excite the electron in the glass to its next level. So the radiation gets absorbed by the glass and never reaches you to give you a sunburn.
Now that’s cool!
Before Modern Physics, I didn’t even know you couldn’t get sunburned under glass. This is just one of the many fascinating things I’ve learned about in Modern Physics, which I definitely recommend every one to take, especially with Professor Smith at Boston University. =]