IPhone 4S Wi-Fi Switch Greyed Out?

I have had this iPhone 4S since January 2013, and I have experienced no problems until recently.

I've looked around Apple support pages, and I have noticed that this is most likely caused by a broken Wi-Fi antenna, and a cause of this could be using the iPhone in a hot climate. Since I've had the phone in January, I have not used in anywhere that would be considered hot - but since four days ago I have been on holiday in the south-east of Turkey, where temperatures have been reaching near 40 degrees Celsius (104 in Fahrenheit). Could this hotter, more humid climate be the cause of this problem?
Would this issue repair itself after being out of the heat for a while, or would it need to be repaired?
Would this problem have not occurred if I did not use my iPhone or Wi-Fi whilst in a hot climate?

This problem seems difficult and/or expensive to fix, and although my iPhone has insurance, I'm still hoping there's an easier solution.

I'm using the latest iOS version available for the 4S (6.1.3), Airplane Mode is off etc., etc. - I've tried all the obvious solutions, plus the 'hairdryer method' several times, but to no avail.

Is there a simple way I can solve this problem from home, or will I need to get my iPhone properly repaired or replaced?

It seems you have already perform all the needed steps before contacting support. It would be wiser to make work the insurance…

That usually happens when there's a fault with the Wi-Fi hardware, either the antenna, or any other part of the hardware which handles Wi-Fi.

Restoring the phone (in some rare cases) fixes it, and if it doesn't, you'll need to take it to an Apple Store for repair because it's a physical hardware issue rather than a simple software fix.