MATLAB: Put block behind colorbar

colorbarcolorbar framecolorbar positioncontourcontourslicefigureMATLABsurfsurface

I have several contour plots on a cylinder that I made in MatLab. In some of them the black text from the colorbar is obstructed by dark colors in the plot. In others, the color of the text is fine so I would rather not change the color of the text. Is there an easy way in MatLab to put a rectangular patch (either white or gray) neatly around the colorbar and the surrounding text but behind it so that only a small amount of the contour is hidden?
I've given a link to 4 .fig files on google drive (they're too big to attach), and a .png of one of them where I put a white block around the colorbar (I would like it to be filled and behind the colorbar but in front of the contour) to show what I am hoping to get.
https://drive.google.com/open?id=14cH1OCuL7-poWk2xckzuETazETpyMm28

Best Answer

I still think repositioning the axis to make room for a marginal colorbar is the cleanest and most efficient approach (see the various position properties of axes).
However, here's how to add an axes under a cloned colorbar. The basic idea is to create a new axis on top of the existing colorbar, set the axis colormap properties to match the main axis, then add a new colorbar to the new axes. Then set the colorbar properties to match those of the initial colorbar. Toward the end of the code below, you can set the transparency level of the new axis. Note that the original colorbar is turned off but still exists. See inline comments for more detail. 
% Open one of your figures
% Get fig, axes, and colorbar handles from current figure
% Assumes 1 axes and 1 colorbar per figure
fh = gcf(); 
axh = findall(fh, 'Type','Axes');
cbh = findall(fh, 'Type','ColorBar');
% Create an axis on top of the current colbar
ax2 = axes('position',cbh.Position,'XTick',[],'YTick',[],'Box','on'); 
% expand the size of the new axis 
% The axis will be 4X wider and its height will be slight larger to make room for title
ax2.Position(1) = ax2.Position(1) - .01; 
ax2.Position(2) = ax2.Position(2) - .01; 
ax2.Position(3) = ax2.Position(3)*4; 
ax2.Position(4) = 1 - ax2.Position(2) - .01;
% The new axis must match the color scale of the one we're imitating
ax2.Colormap = axh.Colormap; 
ax2.ColorScale = axh.ColorScale; 
% set colorbar in new axes (you can add other important properties as needed)
cb2 = colorbar(ax2); 
cb2.Position = cbh.Position; 
cb2.FontSize = cbh.FontSize; 
cb2.Limits = cbh.Limits; 
cb2.LimitsMode = cbh.LimitsMode; 
cb2.TickDirection = cbh.TickDirection; 
cb2.YAxisLocation = cbh.YAxisLocation; 
caxis(ax2,cbh.Limits)
% Set title of colorbar
th = title(cb2,cbh.Title.String,'Units','Normalize');
th.Position(1) = th.Position(1) - min(0,th.Extent(1)-.00); %Move title to fit on axes
% set transparency of new axes (undocumented)
%                   v---transparency (0:1)
ax2.Color = [1 1 1 .6];
% Turn off old colorbar (keep it around in case you need to reference it later)
cbh.Visible = 'off';
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