What temperature is considered to be too hot to take a newborn outdoors for a 30 minute walk or a light jog (shaded by the stroller's canopy, of course)? Can I exercise with a newborn during the morning hours when it is 95 degrees or less? What about using a spray bottle to mist the baby off when it is 95 degrees? Or using a cooling blanket?
Newborns are very vulnerable to extremes in temperature. Not only do they lack the ability to sweat effectively to get rid of excess body heat, but their rapid rate of growth means that they naturally generate more internal body heat than older children or adults.
Furthermore, the sun protection a newborn needs: hat, glasses, and tightly-woven clothes, means he will be relatively overdressed for the heat. Finally, a very young child can't indicate thirst, so nurse or feed Baby once home, or stop if she indicates she's hungry.
Rather than relying on a spray bottle or blanket, it's best not to let a very young child get overheated in the first place.
While I can't give you a specific safe temperature (which would also depend upon humidity, shade, reflected light and the size and maturity of the child) I would advise you to play it very safe. Having said that, your local pediatrician may be able to tell you of indoor or safer exercise options.