If you want to remove the colorbar, you can set the ColorbarVisible property to 'off':
h = heatmap(magic(5));
h.ColorbarVisible = 'off';
Alternatively, use the colorbar command:
heatmap(magic(5))
colorbar off
Heatmap does not provide any control over the borders around each cell, so if you want to remove the borders, you will have to switch to a lower-level function like image or surface.
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