You should be able to do it by setting a percentage height.
We currently do that for both width and height in two of our HTML iFrames using the following code (Google MyMaps iFrame)
<iframe src="https://www.google.com/maps/d/embed?mid=xxxxxxxxx_xxxxxxxxxxxx" border="0" width="100%" height="96%"></iframe>
So what you would need to do is inspect the iframe which is generated by that script, and add the CSS to match it.