What does the white icon mean?

The status is Heat Stroke. Per the wiki:

This status occurs, on the Scorched Earth map, by being overheated, for too long, without resolving the issue. As heatstroke progresses, you will eventually (50%) be prevented from sprinting and (~80%) start to have cloudy vision and drunken swaying movement, and finally start taking health damage until you die.

Unfortunately, the icon is currently missing from the wiki

But this is also confirmed by a reddit thread and various youtube videos

It is the symbol for hyperthermia. If you hold the back button on Xbox it will have text where the icon is telling you that it is hyperthermia and at 1% or however long you have it. And as the previous comment from Timmy, the H key on P.C.