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To answer your question (for the second time) I've had dogs for 40 years, so I'm pretty sure I know the difference between one that has gone limp and is panting heavily, and one that fancies a bit of pampering in the bath. I'm confident most people would.
I think you're overthinking this, and I doubt it has much to do with dogs' intelligence. Some dogs eat stuff that makes them vomit, some dogs eat stones and fuck up their stomachs, dogs do things that make them sick. I've had a dog with a completely ruptured ACL, that would floor most, running and jumping. Dogs are dogs and don't always know or do what's good for them.
Wow. It seems many dogs are even stupider than I gave them credit for.
I guess my immediate question is whether you're misinterpreting the signals/symptoms, surely no animal can reach a point evolutionarily whereby they genuinely risk their health via exposure to the sun? I guess maybe domestication has bred this instinct out of them by restricting their movement so much but it still feels unlikely.