From the Arduino side: dead easy.
From the process side: not so much. Your biggest problem is to make sure the heat is distributed more or less evenly through the tank. It sounds like the stuff can get solid.
Now if you have your temperature sensor on the opposite side of the tank, the heater can be heating the stuff to boiling point while at the sensor's side it's still a solid.
If you have your temperature sensor right next to the heating element, it will melt only the little bit around the heater and then think it's done.
Of course this are extremes, but I'm sure you get the point. If you can keep it liquid at all times, and have some way to get the heat to be distributed evenly (thermal convection of the heated oil may be enough; otherwise you need some form of stirring/pumping/mixing/whatever), it's a lot easier. You may still need multiple sensors to make sure your oil is all at a high enough temperature to be liquid.