You can set the elements of T beyond a certain distance from the origin (i.e., the center of the circle) to NaN so they don't show up.
% first, make a rough approximation to your initial
% image because I do not have your data:
r = 5.7;
x = -r:0.01:r;
y = -r:0.01:r;
[X,Y] = meshgrid(x,y);
T = (X.^2+Y.^2)/r^2;
surf(X,Y,T,'EdgeColor','none');
view([0 90]);
set(gca(),'CLim',[0.3 1]);
colormap('jet');
colorbar();
xlabel('X');
ylabel('X');
title('Thickness');
% NaNs don't show up in the surface plot, so to make the region outside the
% circle disappear:
T(X.^2+Y.^2 > r^2) = NaN;
% and plot it the same way (but make the axes invisible)
figure();
surf(X,Y,T,'EdgeColor','none');
view([0 90]);
set(gca(),'CLim',[0.3 1],'Visible','off'); % turn off the axes
colormap('jet');
colorbar();
