If the hot-air treatment works, I guess it's because your problem came from use of Lead-Free Solder in manufacturing.
The world electronics assembly industry was forced to switch in mid-2000's from tin/lead solder to Lead-Free (mostly just tin) Solder. That led to many quality problems. Not enough research had been done. Lead-Free Solder is very particular about how it's used and treated, or you end up with bad joints, or short circuits (over time, from tin whiskers). The industry eventually learned, after a few years. Unfortunately, some products made during the mid-to-late-2000's that had passed QC and got shipped out, then failed after some years of use and stress (thermal cycling=turning on/off, humidity, bending, etc.).
Lead-free solder melts around 425 deg-F. But a lower temperature like 300 deg-F can solve problems - relieve stressed joints, close small cracks. This is what the internet videos are doing -- with a hair-dryer or oven.
Tin whiskers is another possible problem. To melt tin whiskers -- each & every one -- you probably need to go to 425 F. That heat could damage certain parts -- battery, aluminum electrolytic capacitors, beepers/buzzes/speakers,... anything with soft plastic. You have to remove these before a heat-treatment.
Instead of high heat, you can take out the circuit board, and use a soft brush and vacuum cleaner to dislodge and suck up the whiskers. Go thru every nook and cranny, especially around the ICs. Be sure to use anti-static tools and work area so you don't 'zap' your electronics. That is, you, the table, and every tool should be grounded.
UPDATE 5-16-16: I had to do the oven treatment twice. (The problem resumed after the first bake, a few days later). The MBP has been working fine now for several months of constant use. But I also did an OS update right after that. The fans run faster now. I'm not sure if I did something wrong in re-assembling it, or maybe Apple purposely tweaked the fan settings for problem-prevention.
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