Point density map in QGIS

You can use a combination of the GRASS tool v.surf.rst for interpolation and than create contour polygons with GDAL contour polygons (available since GDAL ver. 2.4). As an alternative, instead of the GRASS tool, you might also use the SAGA tool Multilevel b-spline interpolation for interpolation. All these tool are available in QGIS.

To demonstrate it, I downloaded a points layer representing temperature measurements from 153 stations in Switzerland.

Version using GRASS

1. Run Menu Processing / Toolbox / GRASS / v.surf.rst and keep default values (especially tension parameter = 40). Select the attrribute representing the value you want to visualize. At the bottom of the dialog window (not visible on the screenshot), check only the box to create an output for Interpolated RST and de-select the eight other ones (you don't need them).

2. Output is a black/white raster. Use Menu Processing / Toolbox / GDAL / Contour polygons (if you have only the option GDAL contours, you can run the tool setting the parameter -p to create contour polygons instead of lines if GDAL >/= 2.4). Select the interval between the contours (in my case: 1).

3. Now apply a graduated style to the resulting polygon layer. Here is what I got, took less than 5 minutes:

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Version using SAGA

Everything as above, except that you use Menu Processing / Toolbox / SAGA / Multilevel b-spline interpolation in step 1:

The output is slightly different, also the interpolated values. This method is better to represent local extremes, it has more small sized details, whereas the first version is more even and balanced over greater distances. So always reflect what you want to represent. Also play around with the parameters and try to understand how they influence the result. The sites linked above are a good starting point.

Compare the two outputs here, same scale. As you see, not only values are different, also the extent of the output is different:

Applying a layer mask (polygon for Switzerland, layer rendering style: inverted polygon), I got this (SAGA output), representing interpolation for temperatures measured at 135 stations all over Switzerland, 25th of Jan. 2021, 16:35 h (Central European Time / UTC+1):

And this is what I get with Kernel Density Estimation (Heatmap), where only the density of the points and no attributes are visualized. Be sure to set the values accordingly for radius and output raster size. Choose a radius long enough so that buffers for neighbouring points will overlap, but also short enogh so that not all (or almost all) points fall inside the buffers. Choose an appropriate value for rows and columns that the raster doesn't get too large: several hundreds or a few thousands normally are OK.Pixel size will automatically adapt: the more pixels you have, the smaller their size will be.