My advice would be to go at least down to an inch(perhaps a #3 or 4) to get to where the dog will be cooler. If the coat is thin, you could leave it longer and still have the dog be cool.
Warning: Rant ahead.
Sorry, I don't buy that "hair insulates them from the heat" story. I never have, and I never will without some evidence. All the dogs I've shaved in the summer(for Florida) were MORE comfortable, more active, and acted less hot than before when they had the full coat(whether the coat was clean and well brushed or not). This has been true for all types of coat, including doodles and nordic breeds.
If the dog needs insulation from the heat... why aren't we putting coats on the dogs without heavy fur for summer? If the dog's internal temp is 101f... and the outside temp is 95f... how is putting a layer of insulation going to make the dog cooler? The dog's own warmth is trapped under that fur.
Dogs are mammals. They may not sweat like humans, but the internal heat is still building up under the fur... the heat from outside only adds to that.
A coat of fur can protect the dog from SUN... i.e. prevent sunburns(if it's shaved down extremely short), or help keep the sun's rays from heating the dog more. But unless you're in a place where the sun makes it way hotter than the ambient temps(i.e. desert or beach style conditions), I don't think sun is going to make the dog hotter than the ambient temps already do.