The name of these silver curtains used to reflect heat energy back outside

As Tester mentions, new windows are the most cost and energy efficient in the long haul. However, the upfront cost is substantial, especially if you want to do a lot of windows.

The concept is the same with all window coverings, add an additional layer of air between the primary window and the covering to slow down the transfer of heat. A single pane window is generally .85 r-value. Verifiable r-value numbers are hard to come by for most of these products, but if you do find some, that will give you a basis for comparison.

Other options:

• Storm windows. This is basically installing a secondary window on the outside. These can be quite expensive, or cheaply made using plexiglass. They are cheaper than new windows, reusable, and transparent. The drawback is that there is still a sizable upfront cost and you have to store them somewhere in the summer.

• Secondary glazing. Same idea, except installed inside. Similar advantages and disadvantages to storm windows. They tend to be much thinner and don't change the look of your house.

• Cellular shade. There are some interesting claims with cellular (honeycomb) shades, some claiming to add well over 2 r-value to a window. These will darken the room some and are still quite expensive.

• Window film. This is the cheap option, unless you have curtains laying around. The main drawback is that it's generally opaque and it's more difficult to reuse year-to-year.

• Heavy curtains. Tried and true method used for centuries. Obviously you won't be looking out these windows.

As odd as it may seem, it's a roof. A bay window roof. In the picture you provide, it's actually a roof for the lower bay window, as opposed to being part of the upper bay window.