Adding some comments on comments.
What seems to be missing from the thread is any data on what temperatures are. Most motherboards these days have some sort of temperature monitor. It's pointless spending money on equipment without identifying if there really is a problem. We're five days on and the pc still seems to be running.
The fan being noisy could just be due to the bearing expanding more than usual in the heat or the blades becoming unbalanced due to uneven expansion.
When the weather gets hot in a climate like England (fairly humid) what you feel is quite different to what the pc feels. Because your body relies on sweat evaporating to keep cool, when it's humid it feels really hot. You will notice the difference at a given temperature if the humidity is 10% or 100%. While heat transfer of solid objects is slightly affected by humidity, generally speaking 10% or 100% is all the same to your pc. Bottom line, you feel the heat more than your pc does.
Removing the sides of the case is generally a bad idea if your fans are still running normally. The air flow from your pc fans is channelled by the case on to the pci cards giving forced cooling. Take the sides off and it's half-blowing out the sides of the case. The pci cards/hdds are now cooled by natural convection which is really useless. If you take the sides off, you have to provide external fans that are going to give a sufficient air flow to the front and back of the case.
Blowing air on to the outside of the case has very limited value. The case may feel hot but the heat transfer is small compared to that provided by the fans in the case. As I mentioned in my other post, you are better off getting the heat out of the room with a fan to keep the inlet air temp down.
If ice figures into any plan, you need to be cooling the inlet air, not the case. If it is humid you may cool the air below dewpoint and end up with water in the pc. Great in Saudi, bad idea in the UK.
Starman*