Answer
The gap in the ring will become wider.
Work Step by Step
When the metal ring is heated, it expands uniformly, as though a 3D picture of it were enlarged on a magical photocopier. The thickness, outer and inner circumference, and gap all expand by the same factor.
Another way to think about this is that the gap will expand precisely as much as the thickness of a metal disk that tightly filled the gap.
In other words, every part of the ring expands by the same factor when heated: thickness, circumference, gap distance, hole diameter, etc.
