ALL silicon based chips can operate in the 80c's at its extremity before the elemental properties starts to melt right away, this is the thermal limitations of silicon based technology. This also explains why the CPU industry has pretty much stagnated the fast 5 years in development, thermal limitations have been reached, not much more we can do with silicon based chips.
In the 70s range, the chip will start having issues with electrical signals being passed along if maintained in this high state for long. This explains why most chip manufacturers do not recommend allowing your computer to run in this state, and possess safeties built in to shut down once a certain temperature has been reached and they are always defaulted in the 70s range. As accumulative damage can occur as a result.
Anything below 70s is considered safe for most of your chips' operating range. Laptops, by design, run hotter than an old fashioned rig, as there isn't much cooling made possible in such an enclosed system with all the parts sitting next to each other. You can only do so much to keep a laptop cool. First generation laptops were designed in such a way it never should have been. It is essentially just another form factor for a tower rig with almost no cooling and as such should never be used for resource-heavy activities. The next generation laptops that incorporates mobile CPU technology is how laptops should have been designed originally. CPUs made to stay cool with minimal external cooling required.
Your laptop showing 62c makes sense. It probably has some dust accumulation, take off the back cover and get rid of dust using your preferred method. I vacuum the dust out utilizing q-tips, not the safest method (vacuuming can generate static electricity if not careful) but it works for me. Most generic laptops not made exclusively for gaming will run this hot while idling at room temperature.
The best solution without replacing the laptop to reduce temperatures for laptops is to clear out any dust at intervals, I do my computer rig at every 3 months, they will accumulate no matter what you do. We shed dead skin, and then they turn into dust eventually. Get a lap-rest platform with internal fans to help cool down the laptop. This is basically "brute force" cooling the laptop and about all you can do with laptops in general. Eliminate factors that contribute to dust build up unnecessarily such as smoking in the house, animals in the same room as the computer to name a few. Anti-dust filtration in your house cooling systems also benefits as it helps to reduce preexisting dust in the room. Maintain room temperature at 70 or below to keep the humidity to a minimum or get a dehumidifier for the room the computer is in if you can't afford the high A/C bill this could result in.
The laptop world as we know it is currently undergoing a massive evolution with such new found chip sets that can remain at such low temps without any cooling systems. With this in mind, I would recommend getting a tablet or a 2 in 1 such as M$ Surface or ride the wave out.