This situation is an unfortunate side effect caused by the following factors:
Rather than insert a charge of inert gas (like argon) between the panes of glass, some manufacturers choose to draw a vacuum inside the window panes. This will sometimes cause the glass to become concave, causing the glass to behave like a magnifying glass concentrating light on your siding. The resulting effect is very similar to burning ants on the sidewalk with a magnifying glass.
Another cause is from the Low-E coating on the glass on modern windows. This coating is doing exactly what it is supposed to do – reflecting ultraviolet light away from your interior space. But it is also directing and concentrating it directly on your siding. Either of these factors cause the intensified light to raise the surface temperature of the vinyl above its melting point.
This is a problem that is happening more and more often with our wise choices of energy conserving building practices. There are a few solutions to correct the situation:
1. Install a good quality window screen that covers the whole window. This will diffuse the light and may reduce the surface temperature of the siding.
2. Install an awning or enlarge the overhangs of the house to prevent/minimize the direct sunshine from hitting the window.
3. If the window is not too high off the ground, a strategically placed evergreen can defuse or block some of the sunshine (I say evergreen because this happens just as often in the winter months).
Do not apply window tinting. Tinting is usually applied to the inside surface of the glass, and that is not where the reflectivity is coming from. Installing a dark tint to the exterior glass can overheat the window causing seal failure, and in extreme cases can break the glass.
Other options are to replace the vinyl siding with a material with a higher melting point like fiber cement, wood, aluminum etc. Higher quality vinyl may be more resistant, but the overall melting point will remain the same.
Your situation may not be as bad as you think. It is a small area that is affected, so changing the siding materials on the firebox may be the best solution, and it could be done in a way that it becomes an accent rather than an eyesore.