Thermodynamics: Is it possible to increase or decrease temperature of a "Source" and "Sink"?

Thermal reservoir is basically defined as a hypothetical body which does not undergo significant change in temperature due to the amount of heat transfer to or from the system. The concepts of sink and source are easy to grasp. 
"Source is a reservoir from which you can extract as much heat to the engine without changing source’s temperature & Sink is also a reservoir to which you can transfer as much heat from the engine without changing sink's temperature".
         
Thermal reservoirs specifically have large thermal energy capacity i.e mass times specific heat. This is basically done to simplify things during our analysis of various cycles. Hence to call a body which has significant change in temperature due to heat transfer to or from the system is essentially taking this simplification away from us and in turn not useful. 
!!SO THERE YOU GO, YOU JUST CAN'T HAVE A THERMAL RESERVOIR WHICH UNDERGOES CHANGE IN TEMPERATURE!!.

............Source and sink are thermostats maintained at particular constant temperature. Their temperatures do not change upon adding or extracting heat from them. Hence. It is said that they have a limitless thermal capacity..........

Let us take an example of the Sun (source)....
Take the example of the Sun to clearly illustrate why the temperature of the sink or source does not change (source). The Sun is the best example of hot thermal reservoir (source). 
The Sun has a very high temperature, so if we take heat from the Sun, even after removing a large amount of heat, the Sun's temperature changes relatively little, almost negligible. As a result, even though we continue to get heat from the Sun, its temperature doesn't change. Thus, we can state that it is impossible to lower the source's temperature.


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