diff --git a/draftlogs/6061_fix.md b/draftlogs/6061_fix.md
new file mode 100644
index 00000000000..8f96f9eb2b0
--- /dev/null
+++ b/draftlogs/6061_fix.md
@@ -0,0 +1 @@
+ - Do not exceed layout font size when `textfont` is set to "auto" for `heatmap`, `histogram2d` and `contour` traces [[#6061](https://github.com/plotly/plotly.js/pull/6061)]
diff --git a/src/traces/heatmap/plot.js b/src/traces/heatmap/plot.js
index 1db9318bd4c..f77f097d066 100644
--- a/src/traces/heatmap/plot.js
+++ b/src/traces/heatmap/plot.js
@@ -453,6 +453,7 @@ module.exports = function(gd, plotinfo, cdheatmaps, heatmapLayer) {
             var font = trace.textfont;
             var fontFamily = font.family;
             var fontSize = font.size;
+            var globalFontSize = gd._fullLayout.font.size;
 
             if(!fontSize || fontSize === 'auto') {
                 var minW = Infinity;
@@ -479,7 +480,7 @@ module.exports = function(gd, plotinfo, cdheatmaps, heatmapLayer) {
                     !isFinite(minW) ||
                     !isFinite(minH)
                 ) {
-                    fontSize = 12;
+                    fontSize = globalFontSize;
                 } else {
                     minW -= xGap;
                     minH -= yGap;
@@ -492,7 +493,8 @@ module.exports = function(gd, plotinfo, cdheatmaps, heatmapLayer) {
 
                     fontSize = Math.min(
                         Math.floor(minW),
-                        Math.floor(minH)
+                        Math.floor(minH),
+                        globalFontSize
                     );
                 }
             }
diff --git a/test/image/baselines/contour_heatmap_coloring_reversescale.png b/test/image/baselines/contour_heatmap_coloring_reversescale.png
index 97cc01d6d91..b14417224c9 100644
Binary files a/test/image/baselines/contour_heatmap_coloring_reversescale.png and b/test/image/baselines/contour_heatmap_coloring_reversescale.png differ
diff --git a/test/image/baselines/heatmap_brick_padding.png b/test/image/baselines/heatmap_brick_padding.png
index b8620ac7c74..41f917be325 100644
Binary files a/test/image/baselines/heatmap_brick_padding.png and b/test/image/baselines/heatmap_brick_padding.png differ
diff --git a/test/image/baselines/heatmap_categoryorder.png b/test/image/baselines/heatmap_categoryorder.png
index a76a54c1641..ced6e1875ca 100644
Binary files a/test/image/baselines/heatmap_categoryorder.png and b/test/image/baselines/heatmap_categoryorder.png differ
diff --git a/test/image/baselines/heatmap_columnar.png b/test/image/baselines/heatmap_columnar.png
index 04d545dea86..14be707733a 100644
Binary files a/test/image/baselines/heatmap_columnar.png and b/test/image/baselines/heatmap_columnar.png differ
diff --git a/test/image/baselines/heatmap_xyz-gaps-on-sides.png b/test/image/baselines/heatmap_xyz-gaps-on-sides.png
index 66aae47f18d..3247642795f 100644
Binary files a/test/image/baselines/heatmap_xyz-gaps-on-sides.png and b/test/image/baselines/heatmap_xyz-gaps-on-sides.png differ
diff --git a/test/image/baselines/hist2d_summed.png b/test/image/baselines/hist2d_summed.png
index 49680d69708..6d7e8eda766 100644
Binary files a/test/image/baselines/hist2d_summed.png and b/test/image/baselines/hist2d_summed.png differ
diff --git a/test/image/baselines/histogram2d_bingroup-coloraxis.png b/test/image/baselines/histogram2d_bingroup-coloraxis.png
index f88342bc1ce..9fed38448d2 100644
Binary files a/test/image/baselines/histogram2d_bingroup-coloraxis.png and b/test/image/baselines/histogram2d_bingroup-coloraxis.png differ
diff --git a/test/image/baselines/histogram2d_bingroup.png b/test/image/baselines/histogram2d_bingroup.png
index 9fc00b968e4..e8b0be607a8 100644
Binary files a/test/image/baselines/histogram2d_bingroup.png and b/test/image/baselines/histogram2d_bingroup.png differ
diff --git a/test/image/baselines/histogram2d_legend.png b/test/image/baselines/histogram2d_legend.png
index 242d4d68d16..2d00c636643 100644
Binary files a/test/image/baselines/histogram2d_legend.png and b/test/image/baselines/histogram2d_legend.png differ
diff --git a/test/image/baselines/zsmooth_methods.png b/test/image/baselines/zsmooth_methods.png
index cf25b9e281e..ce62857e007 100644
Binary files a/test/image/baselines/zsmooth_methods.png and b/test/image/baselines/zsmooth_methods.png differ