S.
You are not a bad mother for wanting your baby to be comfortable. As long as he is loaded up on sunblock, he will be fine. I will say though, that it is a common misconception that the less clothes, the cooler you will be. If you notice construction workers working out in the middle of the afternoon with longs pants and lonsleeve shirts, it is for good reason. The clothes(cotton, because it allows air in) absorb your sweat and become damp, which keeps you cooler and the benefit is you protect your skin from the sun. I found a little cloth hat and I get it a little damp before we go to the park and it really helps keep my baby cooler.