Dogs have a higher surface-area-to-volume ratio, which helps, though the fur of course hinders.
On a related note, I've speculated for years that tongues play a major cooling role for whales. These are highly vascularised structures which can be exposed to tremendous water flows (for effective thermal transfer). The animals otherwise have an immense metabolism, and are largely quite well insulated by blubber. And of course cannot effectively sweat. Even if the usual problem is heat retention, highly-energetic activities (long-distance migration, escape from or combat with predators, feeding activities) might result in excess heat which needs to be shed quickly. As a long-time swimmer myself I've experienced overheating even in relatively cool waters (for humans) and the challenges in reducing core temps. There have been multiple cases of open-water swimmers overheating and even dying swimming in warm temperatures (several in the middle-east over the past decade or so).
I'd just written that I'd found no scientific literature discussing this when I attempted another search (using FastGPT from Kagi, which I'm finding quite useful for this sort of thing). And lo! Two hits:
"Thermoregulation in the mouths of feeding gray whales" (1997)
<https://pubmed.ncbi.nlm.nih.gov/9353198/> doi: 10.1126/science.278.5340.1138.
"The blood vessel network in the tongues of gray whales precools blood to avoid heat loss via counter-current heat exchange." <https://asknature.org/strategy/lingual-rete-precools-blood/>
This actually discusses structures of the tongue which reduce thermal transfer, but also specifically addresses the characteristics of the tongue which make it effective at thermal transfer:
Baleen whales such as the gray whale move huge quantities of cold ocean water through their very large mouths and across the filtering surface of the baleen. The tongue of a whale can represent as much as 5% of its total body surface area. The whale’s body is well insulated with blubber but not the tongue. Thus, to avoid losing too much of its body heat to the cold water passing through its mouth, the gray whale’s tongue has the largest counter-current heat exchanger yet described.
I feel vindicated!