Cookies spreading much more on the second tray than the first

Baked two trays of the same chocolate-chip cookie dough, 12 minutes apart. First tray: thick centers, lightly browned edges. Second tray: flat discs with crispy rims. Same scoop, same oven setting, same parchment brand. The dough sat on the counter while the first tray baked, and I reused its still-warm metal sheet. I suspect the hot pan melted the butter before the cookies set. Would chilling the second set of dough fix this, or is a completely cool tray essential?