Unfortunately, you're a victim of the recent penchant of TMW to lock down these higher-level graphics objects so that the underlying axes handles (or the colorbar handle here in particular) are not only hidden but made private so not even the magic from Yair Altman's getundoc function can find the handle.
Nor can you do anything exciting like not show the builtin colorbar but then add your own so that you could use its properties--
Error using hold (line 59)
Using hold with heatmap is not supported.
Well, what happens if go ahead anyways...
Error using matlab.graphics.chart.Chart/colorbar
Output arguments are not supported when using colorbar with heatmap.
It simply traps the call and resets the 'ColorbarVisible' property back to 'on'
Well, one last thing to try...
>> hT=text(20,8,'Text Label','Rotation',90,'HorizontalAlignment','center');
Text cannot be a child of HeatmapChart.
Well, one more try...
Error using heatmap (line 78)
HeatmapChart cannot be a child of Axes.
So, can't even put the heatmap into a subplot...
I've railed about this sort of thing over many of the new features; all I can suggest is to add your voice to the chorus of discontent with this misguided direction of taking full control away from the user--"Mathworks Knows Best!" seems to be the new mantra and users are children to be protected instead of being given the toolset.
I still think it a very rude thing TMW has begun doing along these lines in not letting users have access to properties they might want to tweak even if the developers believe they've done the best possible design. It's still possible to have the simple-to-use case with default parameters but still let the user adjust to suit; there's no reason for making all these oddball figures that don't match the general pattern of a handle graphics axes object.
Anyways, still yet one more try shows a way on can make it work -- use two panels in the figure instead. The following still needs work to fix up the color range and adjust the sizes, and it may not be worth the effort in the long run, but is only way I can see to get the desired effect and still use the builtin heatmap.
hUIP=uipanel('Position'=[0 0 0.8 1]);
hUIP(2)=uipanel('Position',[0.8 0 0.2 1]);
hCB=colorbar(hAx,'Position',[0.15 0.11 0.15 0.815]);
hCB.Label.String='This is Colorbar Label';
hCB.Label.Position=[2 0.5 0];
The above yields
As noted, it still needs work to adjust panel sizes, position of colorbar and the colorbar range to match, but the basic objective is doable -- albeit with much more effort than what should be needed.