Howdy sellcellgroup, true cell phones heat up, but not all of a sudden to the point of not being able to hold it.
If the problem started suddenly after a year, it is either a battery problem or a short. Since cleaning the battery terminals worked, it may well have been a short created by the "black stuff" which sounds like some form of corrision to me.
As someone suggested, it may be time for punit12, to replace that battery. As there really should be no reason, with normal use, that a battery should have or produce "black stuff" on the contacts of the battery or the phone itself.
Old batteries can be prone to leaking, especially if there is any sort of over charging/heating problems. Corrosion, can cause shorting and over heating problems, which can lead to a battery exploding while being charged (had this happen to an RC car). And the corrosive goo from a leaking or exploded battery on the circuit board, contacts, plastic and any wiring inside of an RC car or cell phone is NOT a good mix.