I have not read all the posts so I am assuming that the oil temperature remains the same when the object is immersed in the oil bath. To keep the oil at a constant temperature, a heating source is required so you should then know the value of the heat input to the oil bath. the amount of heat absorbed by the block will then be equal to the heat input to the oil bath and we are discounting all heat losses to the environment. So far for equation, we have:
Qin= M*Cp*dT/Dt; Qin (but/hr),M (lbm of block), Cp (Btu/(Lbm-dF),dT/dt (rate of rise the object temperature in degrees F/time element be it sec,min,hr)
All units are in the English system and it's up to you to convert into the Metric units. The equation that I presented is emendable to a spread sheet. You could also use integration for a solution. I would use both as a mean to determine accuracy.