They are jpg images in some sort of Thumbnails folder, as I remember. Do a search in your ADE folder, and perhaps in your Documents and Settings folder (XP, use the corresponding folder name for later OS's).
ADE has a simple built in screen capture tool. This can be used to capture and save thumbnail images of library objects and generic buildings. The screen capture tool is available when you see a button like one of these:
Click this and ADE will hide itself. The main screen will change slightly. Position the mouse at top left of the area to capture, left click, hold down and drag out a rectangle for the captured area. Release the left mouse button. The rectangle will remain on the screen. If you do not like what you have then just draw another rectangle. When satisfied hit the space bar to capture the image and return to ADE. Hit Esc at any time to close the screen capture tool and return to ADE without taking a screen shot.
Make sure FSX is in Windowed Mode
If you have multiple monitors then the screen capture may not pick up on the monitor where FSX is located and you may need to move it. You can always cancel the screen capture by using the Esc key.
There have been one or two reports where the screen capture tool does not appear over whatever is on the monitor. This should not happen but if it does then there will be a tab for 'Screen Cap' in your task bar – click that to bring the capture tool over everything else.
ADE requires that the image be in jpg format and that the name contains the full guid of the object in FSX format.
Where there are a large number of thumbnails available ADE may take a second or so to find the appropriate on for an object. ADE has an 'on-the-fly' indexer for thumbnails. The first time you mouse over an object it may take a short while for the tooltip to appear. However once ADE knows where the thumbnail file is it indexes the information and the appearance of that thumbnail should be instantaneous. On-the-fly indexing also take place anywhere a thumbnail is displayed so over time more and more are indexed and the delay in seeing the tooltip etc should be minimized.