I also have this same issue. It's a real shame that Apple would release an update for phones that cannot properly handle the firmware. If they tested it like they should have, then this is clearly a message from Apple stating "get a new phone or leave us."
There are some options that people have to deal with this prevalent issue.
1) Find an iphone that is pre 7.0.6 (I started having this issue at that update) and NEVER update it (regardless of the "security issue" that 7.0.6 supposedly solves.
2) Replace the wifi-chip. There's a few youtube videos that show how to do this (you'll find some using search terms like "greyed out wifi"). It may make more sense to just have a professional do this for you.
3) The heat/freeze. As someone else previously stated, this is a bit "radical," and should be done with caution. DISCLAIMER: I'm SOOOO not responsible if you manage to break your device beyond repair.
What it entails: Use a blow dryer (I used a heat gun) to heat up your device, concentrating mostly at the top of your phone where the camera and speaker is. Obviously don't put your heat source directly on the phone, keep it maybe an inch or three away. Your phone is SUPPOSED to give you a temperature warning (at which point you would cease heating the device). Mine did not, so I checked it by hitting the home button and was greeted with half a black screen and the other half completely fine. Almost had a conniption.
I decided at that point that it must be hot enough, so I turned my heat gun off, and held the power button down. INSULATE YOUR HAND, lest you burn yourself when holding that button. Once I saw cancel ("slide to power off was hidden in the black part of the screen), I slid my finger over where I imagine the "slide to power off" was, and it turned off. Quickly pop that sucker in a zip lock bag and leave it in the freezer for 10 minutes.
Pulled it out after, screen back to normal. Wifi functioned and still functions normally (updates were a bit wonky, had to update each app 1 at a time instead of "update all"). I'm assuming that this is only a temporary fix, so I suggest that if you don't want to do it again, don't let your phone get too hot EVER. Don't use it too much, yada yada. OR, just avoid this altogether and go for option 1 or 2.
Apple, I'm pretty disappointed in you.