Black slaves died at a much higher rate than whites. I'm not sure how much heatstroke was a cause, but anecdotal evidence suggests it was. Planter Thomas (no relation to Ben) Affleck writes: "Quarters are often badly located; children allowed to be filthy; are suckled hurriedly, whilst the mother is overheated; are laid on their backs when mere infants on a hard mattress, or a blanket only, and rocked and bumped in badly made cradles; not a few are overlaid by the wearied mother"

• Thomas Affleck, “On the Hygiene of Cotton Plantations and the Management of Negro Slaves,” Southern Medical Reports 2 (1851): 435

There is a pretty extensive medical history of the civil war, for example "The Medical and Surgical History of the War of the Rebellion.", volume 1 part 1 has death by disease estimates for white and black Union troops. The figures are broken down by department and it is difficult to compare like to like, but it doesn't seem like sun-stroke affected white troops more than black or vice-versa. That said, the two groups often faced very different tasks, so comparing disease mortality and morbidity should be very difficult.