The problem with heat build up is probably not as much due to your window as it is to the expanse of roof above that room. I had a similar problem and a friend of mine who's a builder told me to call SECO, our local electric company, to find our what they recommend for the heat build up problem. They gave me to their home energy efficiency dept. The SECO rep in that dept said they recommend a radiant barrier in the attic. They futher told me attic fans do little to nothing to dissipate the heat. They also gave me the name of the installation company they recommend because SECO (a cooperative) knows this company does the installation correctly.
Energy Home Shield
The whole attic installation cost me $2,000, but it made an immediate and huge difference in lowering the temperature in the whole house and especially in that sun exposed room. SECO said the energy savings would take about 6 years to recover the cost. So, if you intend to to stay in your house at least that long, I concluded it's best to spend the money now, rather than waste it on dozens of other methods that in the end prove ineffective.