STOP!! Disconnect your MagSafe charger and turn off your system as you could make things worse!
First thing here is to make sure the MageSafe cable is not frayed or damaged if it is you need a new power adapter.
As to the next step we really need to know which model you have.
Can you give us your serial number so we can look it up or you can do it you self using this web site: EveryMac, then alter your equipment choice to reflect your system model. Or, just tell us which is yours.
First it was not new but used, it could have even been stolen. So the seller mis-lead you if they told you it was new (no previous owner).
Did you spill something into the keyboard or sit the system down on a wet surface?
I would stop using smcFanControl software here are in the long run you end up doing more harm then addressing the root issue on why the system is overheating. In fact your current problem could be related.
For now we need to inspect things internally. Are you up to fixing your own system here? Do you have the needed tools and an antistatic pad and wrist strap?