That's hard to say.
I do not intend to humiliate an idea if it is based on a technical calculation.
It is expected that the manufacturer uses the guaranteeing components
stable operation at working temperature.
The processor itself has its own specifications and requirements for active or passive cooling.
The device manufacturer then calculates passive or active cooling.
The receiver is based on passive cooling
and they certainly counted on a certain processor temperature and other components.
Otherwise, thousands of receivers will be in service after three months of use
in summer conditions.
Let's say for example
some of the components in the TVs are getting hotter than in the receiver
and there is no fan.
Of course, if the receiver is indoors
without good air circulation or in a room where the summer temperature is high
then extra cooling can prolong the service life.
However, in other cases (room temperature abt 21 C and free circulation of air) it is questionable whether it has any significant influence.