So, you need a temporary solution to cool off your GPU temperature, but you don't need to spend money on it !. Well, the current cooling system that you have can't give you the results that you need. So, you need to think out of the box.
I have a bit of crazy idea, but I am sure that can give you the best results.
First, since the computer case is a mid size, the CPU & PSU fans are too close from the GPU, which means that their hot air will heat up the GPU, since the fan of the GPU will only pull in that hot air, because there is no cold air around it. ٍSo, @Matthew has described it in his answer, and I agree with him. That's one of the things that I always consider in choosing computer towers, which is the space between CPU, PSU, and GPU. Which is important in airflow.
Secondly, you may consider to generate a cold air manually not depending on the computer fans only. What I mean of that is to maintain the room temperature and also the location of your computer tower where it stands.
Lastly, my idea is that you can use any fan that can be found at your home not necessary to be built for a computer, and it should do its job. Surly, it'll be noisy, but it'll be effective solution. You can even rebuild it to suit your case. Also, if you want to be more creative, you can use water container and fill it with car radiator fluid which will cool the fan air. this will make it like a portable AC. You just need to think of a way to do it from the useless stuff around you. All you need is just a fan, cartoon box, bottle, and water. You can build it with your computer fan or a home fan.
Just think out of box.
This is what I have, hope it will trigger something that guide you to your goal.