In this case the expansion is totally free.
The diameter D is the longest straight dimension this will increase to D(1+aΔT)
So the circumference (which is the longest dimension) will increase to πD(1+aΔT).
However the angle subtended to the centre by the gap cannot increase since a full circle must still contain 360 degrees.
So yes the gap will increase and this should be enough information to calculate this change.