If you're keeping all your funds on exchanges, I'm willing to bet you now you will lose a significant portion within 2 years. I try not to hold much money on exchanges, and I've lost money on at least 4 sites that have been hacked (and these weren't minor exchanges, they all had significant name recognition). If you're holding much in bitcoin, I strongly recommend you use a cold wallet for the amounts you don't need to access frequently. A cold wallet shouldn't damage your laptop as it doesn't use any cpu power normally, so no overheating worries.
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No, turning off internet won't cause the coins to be lost, although you can't spend them until you turn it back on. Similarly, you can turn off the computer and your coins will still be safe. In fact the cold wallet I recommend involves keeping your main bitcoin holdings on a computer that never connects to the internet.