Suppose we are working with a Carnot engine. In this engine, temperature of the heat source is say $373K$ and that of heat sink is say $293K$. Now, the initial temperature of the gas(ideal) is 333K. The gas is isothermally and adiabatically expanded, and its temperature was reduced to 313K, and again the gas is compressed adiabatically and isothermally raising its temperature to 333K. So, a reversible cycle is completed. Now, if we calculate the efficiency of the engine then we will obtain, efficiency=1-Q2/Q1.
Here, Q1→heat absorbed in isothermal expansion step
Q2→heat rejected in isothermal compression step.
We know that in case of ideal engine/carnot engine heat is proportional to temperature which is in our case Q1∞333K and Q2∞313K as per the decription in the link below:
But as per the image attached below this shows that Q1∞373K(temperature of the heat source) and Q2∞293K(temperature of the heat sink).
So my question is when the cylinder comes in contact with the heat source is it let to increase its temperature to that of the temp. Of the source or it can be any temperature? If it can be any then why does most of the books and articles state that efficiency of the carnot engine is dependent on tbe temperature of heat source and heat sink?