In this particular study, runners completed 3 treadmill runs to exhaustion in a warm environment: One trial was precluded by a 20 min warm-up, one wearing a cooling vest for 20 min, and one "without particular preparation."
Runners ran for 32.5 minutes after pre cooling, 26.9 min after the 20 min warm-up, and 30.3 min after doing nothing. Effects of warm-up and precooling on endurance performance in the heat.
In this small study that controlled for increase in body temperature, runners did better on a 4 min maximal treadmill run with lower levels of lactic acid produced and a higher blood pH maintained (blood pH decreases when lactic acid increases). Effects of active, passive or no warm-up on the physiological response to heavy exercise.
MY COMMENT: Adjust your warm-up to the conditions, and do whatever you can do stay cool: stay inside if an air conditioned room is convenient, jump in a lake, or take a cold shower).