Definitely don't shave your dog in the summer.
Unlike people, dogs only have the ability to sweat through their paws, not their whole bodies. They have two mechanisms to help them cope with the heat: panting and their fur. The fur helps trap air between the layers, which helps regulate the body temperature at the skin level to some extent.
In order for that to work properly, the fur should be brushed frequently to keep it free of mats, tangles, dirt, and anything else that shouldn't be there.
When you shave a dog, you actually make them more sensible to the heat because you're taking their fur's protection away, both in terms of its regulatory function, but also in terms of sun protection. When a dog is shaved, they are much more susceptible to sunburn. Their bellies are particularly sensitive if you walk on a surface that reflects heat / sun like asphalt roads, tarmac at an airfield, and the like.
There are a couple of things you can do to help your dog feel more comfortable in summer beyond brushing.
The first is to get your dog used to the warmer temperatures - dogs, like humans, can adapt to temperature / climate changes by being exposed to them more. If you normally keep the temperature in your home at 72 degrees, consider turning your AC off and putting a fan on instead, or setting the AC higher so it doesn't kick in until it gets to 80 or 90 degrees. That helps get your dog's body (and your own) used to the hotter temperatures.
The second thing is to really be on top of watering your dog, especially when you are exercising or hiking. The rule of thumb for humans in the middle of summer is that you should drink one cup of water every 15 minutes when exercising in the heat. A good rule of thumb for dogs is to offer them water every time you have it. I taught my dog to drink from a water bottle / canteen, so we don't have to stop long to unpack water bowls, etc.
The third thing is to cool your dog off whenever it is needed. If your dog looks like he's overheating or is panting heavily, then it's probably a good time to cool him down. Use cool water, never ice cold (freezing water is too much of a shock to the system) and cool down the sides of the dog's chest, stomach, and inside of the rear legs. Those are the areas major blood vessels run through. Cooling those areas will help the whole body cool.
Lastly, there are a number of cooling products you can use to help your dog stay comfortable in the heat. There are cooling neckbands or bandanas, cooling mats, and a variety of cooling vests. I tested a number of those products last year and you can read more about my Summer Safety test and reviews for the products I tested here - http://abbyk9.blogspot.com/2007/07/summer-heat-study.htm