It has nothing to do with translation, it all about relative temperature differentials. If you look anywhere in space but the sun the absolute temperature is about seven degrees above absolute zero, −273.15 °C or −459.67 °F. Since the earth's surface is much warmer then that we loose heat by radiating it into space. The sun is much warmer then earth and we gain heat by intercepting heat radiating from the sun. If the sun cools down we receive less heat so we cool as well.
It rather like sitting around a campfire, the side facing the fire feels nice and toasty and the side facing away gets chilly.
Regards,
GtG
A dying fire does not “cool” you...it just doesn’t warm you as much. The heat radiates out (well, convects and conducts by a campfire, but radiates with the earth) and is not replaced as much...but the sun doesn’t “cool”... That’s why the phrasing seemed odd.