This study, in the Journal of Applied Physiology from 2004, explored whether a cooling vest worn during an active warm-up enhances 5-km run time in the heat. Seventeen competitive runners (9 men and 8 women) completed two simulated 5-km runs in a hot, humid environment (32°C, 50% relative humidity). The athletes completed active warm-ups during which they wore either a T-shirt or a cooling vest. Results showed the 5-km run time was significantly lower (by 13 second) for those who warmed up in a cooling vest, with a faster pace most evident during the last two-thirds of the run.
Rectal (Tre; A), esophageal (Tes; B), mean body (T̄b; C), and mean skin (T̄sk; D) temperatures during the warm-up and the simulated 5-km run. Values are means ± SE. Vest, experimental condition in which subjects wore a cooling vest with ice packs during warm-up. Control, condition in which subjects wore a regular T-shirt during warm-up.
You can access the study here.