It’s the Nathan RunCool Ice Run Hat: Nathan RunCool Ice Run Hat. Cap with Stash Pocket for Ice. Stay Cool While Running. https://www.amazon.com/dp/B07W81L18R/ref=cm_sw_r_cp_api_glt_fabc_N1PMGZE1XFFNH9DEYJX5
Love this hat. I have one, just got it this summer. I put ice cubes in it and keeps my head cold for about 30 minutes (come in different colours):
Once he runs longer than 45 minutes at a time in humidity, hydration can be critical . I would suggest a hydration belt for shorter runs (in the summer) and longer runs in the cooler months. A running vest is great too but more expensive.
Vest (make sure you get the correct size): https://www.amazon.com/Salomon-Unisex-S-Lab-Racing-X-Large/dp/B01HNU5LSK/ref=sr_1_1?crid=2NNX4Y4JRYADU&dchild=1&keywords=salomon%2Bs-lab%2Bsense%2Bultra%2B5%2Bset&qid=1599532810&sprefix=salomon%2Bs-lab%2B%2Caps%2C152&sr=8-1&...