First, you need to generate the sequence that you want to export. Do this by following the process for creating heatmap replay animations which allows you to select time boundaries and the numbers of frames per second you want the heatmap replay animation to run at.
The movie export is in essence a built-in screen capture tool, so you can adjust the heatmap settings including intensity/radius/blur and the zoom to focus in or out at your desired level. You can also adjust the speed of playback using the mini-scrub bar at the lower left of the screen.
Once you're happy with all the settings and the framing of the animation, hit the 'Export heatmap' button in the left hand menu:
You will then see the following confirmation message:
Once the MP4 file has been generated you can download it from the Downloads section (click on the cog icon in the top right corner of any screen to navigate there).
The MP4 file will be in a sub-folder call "Video" and will have a long file name based on its date-time parameters.