you don't have a lot of options with the scenario you've given.
is it impossible to leave the dog in the trailer with the generator running and air conditioner turned on?
we do this with our Lhasa if we cannot take him with us.
but with two of us, we usually take him along and one of us stays with him to run the car's a/c or get him out on a leash and find a shady spot to wait.
maybe you can find a dog sitter in the park. maybe there's a kennel close by that will take him for a couple hours. or a pet salon...get him a bath and manicure while you're gone :)