I barely know your specs and I don't even know how you temporarily fixed it in the help thread (also in case anyone runs across a similar problem). I didn't even know you have a laptop and those are more difficult to fix than a desktop (a desktop randomly turning can be a multitude of problems that may have to do with some faulty parts that you may need to replace like a broken fan or a wonked out power supply unless you have a motherboard issue and in that case you're sorta scull fucked and you should probably buy a new computer for a new motherboard). Your laptop wanting to turn off at random points sounds like an overheating issue to me, have you checked its internal temperature with a program?
Hot days are rarely, if ever, the cause of overheating computers. Overheating is caused by a multitude of factors, such as a bad fan, heat sinks not working, lack of thermal paste, etc. Whenever a computer detects that its temperatures are reaching dangerous levels, it shuts itself off to prevent damage to vital components.