Most models of iPad require a Power Adapter rated at 10-12W (i.e., 2.0-2.4A @5V) or greater to reliably charge.
5W Power Adapters intended for older models of iPhone are inadequate to charge an iPad; if the iPad charges at all, charging will be very slow. If you do use a low-output Power Adapter, while it will be unable to charge or maintain the iPad, the Power Adapter and iPad will suffer no harm.
Power Adapters will usually run warm (or very warm) while connected to AC-power and are charging a connected device. This is entirely normal and as expected; heat is an inevitable byproduct of power conversion. The temperature of the Power Adapter (and your iPad) will usually fall when the connected device has reached full charge.
While an otherwise healthy iPad and Power Adapter will suffer no harm when connected for extended periods, leaving them unnecessarily connected to AC-power is not recommended. As with any device, in the unlikely event of a fault occurring, they may suffer damage to both themselves and surrounding materials. Also consider the environmental and cost impact of continuously leaving AC-powered items connected to the mains supply.
Be aware that many computer USB ports cannot source sufficient power to charge an iPad. Unless explicitly designed for charging connected devices, computer USB ports are typically limited to 0.5-1A @5V (i.e., 2.5-5.0W).
For peace of mind, if you have any concern at all for the health of your Power Adapter or iPad, consider visiting the Genius Bar at your local Apple Store or Apple Authorised Service Provider (AASP). Here the technicians will be delighted to test and assess your Apple devices and Power Adapter(s):
Genius Bar Reservation and Apple Support Options - Apple