It's a good idea to put a laptop on a table or desk if you can, rather than your actual laptop. Quite apart from the heat - and there have been some nasty cases of burns, where people have fallen asleep - the laptop is situated very close to the reproductive organs, so not a good place to put it. (This is where old-fashioned books score - no heat radiation from a book!).
Short periods may have little or no effects, as any radiations from the laptop hardware are 'soft' radiation, and more likely to cause heating than deep penetration. But not good to have close to your body for any length of time.
When the laptop is transmitting by wireless to and from the router, as it will be all the time you are on the internet, this is similar to holding an in-use mobile phone close to your body all the time - not a good idea. Some studies suggest habitual mobile phone users are more prone to ear and associated cancers. So far as I am aware, nobody has done a similar study on the gonads yet.
The laptop is best used on a tabletop. That way only your hands are really close to the laptop, when you are typing. You can always plug in a mouse, and use this instead of the touchpad. Many people prefer doing this anyway, and there should be plenty of room to use a mouse at a table.
You can also plug in a keyboard if you wish, if you maybe do hours of typing. That way you are a bit further away from the laptop when typing, too.
As treestump mentions, it is safer to use a ethernet cable from the router to the laptop instead of using wireless if you can. The signal is usually much quicker anyway, as cables don't drop signals like wireless does. The cable (Cat5, or Cat5e) is well-shielded, so there is very little emf output from the cable.
I would have reservations about telling people not to buy S/H laptops. There is, if anything, less shielding on a modern slimline laptop than on the more 'clunky' models of a few years ago. 'Slimline' means there is less bodywork between the operator and the hardware inside; this generally equals less shielding. This is because little or no regulations exist to measure bio-damaging radiations from laptops. The regs which do exist mostly concern how the laptop should not interfere with other existing electrical equipment in the vicinity.
If you must use a laptop on your lap for an hour or more, womble an old stainless steel tray big enough to set it on, and use that. It will absorb and dissipate heat from the laptop to a great extent. It will also provide a minimal amount of shielding to your vital parts.