If I remmeber glass has impurities that block infrared, as pure SiO2 transmits it to some degree.
Btw. the sun light can heat you through a glass window because other wave lengths can heat object too. Blue light is highly energetic foe exemple, an so if absorbed it gives a lot of heat, although in natural light it is not predominant by intensity (# of photons per second).
Long wavelength infrared doesn't penetrate glass because of the molecular-level IR absorbance of the silica. Silica has a *very* strong band at around 1200 cm-1. This band blocks > 99% of the light at that frequency even at very low concentrations (i.e. a few mg of ground up glass in a KBr pellet). So, when you have the bulk material, that band is extremely broad, and produces complete extinction all the way out to ~2500 cm-1 (about 4 microns wavelength), and down to < 200 cm-1 (~ 50 microns). There is another strong band around 3500 cm-1 for the surface terminated Si-OH bonds, but there are no significant absorptions in the near-infrared (i.e. from 4000 cm-1 up to the visible, which starts around 13000 cm-1 or so). The latter point is why you can still feel radiant heat through a glass window pane, as you suspected.
It should be noted that there are many different varieties of silica/glass/quartz, and all of them have different transmission properties, however, non of them transmit to any significant extent at photon energies below 2500 cm-1, as far as I am aware.
Ive always wondered why something as dense as glass or water is transparent
It comes up a lot here - it's probably in the sticky thread, do a search for a more complete answer
In simple terms a photon excites an atom (strictly a bond between atoms)
This then de-excites emitting a new photon. the trick is that in a crystal the atoms are arranged in a regular pattern so the new photon goes off in the same direction.
Glass is a bit tricky, the atoms aren't in a regular pattern like a diamond but they are fixed
In a metal there are lots of free electrons on the surface which absorb any photons, but because these aren't in a regular pattern the emmitted photon goes off in a random direction - so metals are reflective.
Also most commercial glass is also made so that any impurities which absorb visible light are removed, to make it as clear as possible.