A common bit of glass mythology is that it flows -- albeit at glacial speeds -- at room temperature.
Is it true? No.
Resistance to flow is called viscosity. Water has a very low viscosity. Ice has a very high viscosity. The difference between liquid water and ice is the strength of intermolecular bonds. Above 32F, all of the bonds break and the water flows. That's because ice is a crystalline material where the molecules are arranged in a regular pattern and the strength of the bonds between them is consistent.
Because the molecular structure of glass is irregular (non-crystalline), the strength of those bonds varies across the material. When glass gets sufficiently hot, the bonds begin to weaken and some break. Heat the glass more, more bonds break, and the viscosity of the glass goes down. Raise the temperature high enough and glass runs like warm syrup.
But those intermolecular bonds do not begin to come apart at any temperature you or I would find comfortable. That means that glass at room temperature, no matter how long it sits, will not flow.
What above those old church windows that are thicker on the bottom? Hundreds of years ago, flat glass was made by cutting and flattening (while hot) blown glass. This method of manufacture was less than perfect and panes of glass were rarely even in thickness. It should come as no surprise that the window installers would usually put the heavier end to the bottom.