I also think that the card does not need an extra cooler. It has been running stably for years, even though it gets relatively hot during operation - the sensor reports between 70-80°.
It would be much more important to make sure that the ventilation in the housing is good enough so that the heat can get out and does not accumulate.

I don't have an extra cooler for this card. It only gets hot when working in 10 Gbit mode all the time. I'm with Swisscom, they have a 10 Gbit modem, but the fastest port is only 2.5 Gbit. So far I haven't had any problems with the heat.