Interesting thought (and I’m a geek so I’m down with this convo!)
My first question though, what heat map tech are you using to measure?
Ok back to it - before making homepage changes, I would generally want to test this somewhere else (A / B testing).
So what I’d likely do is take one of my high traffic pages (or if using PPC the PPC team could help with this by creating a duplicate homepage) and I would test the various options (with header image, no header image) whatever permutations you’re considering.
Some (many) options / combo’s are available out of the box - but if you wanted to test more refined mods like “half size image height” as you reference above that would require retainer time since you’d be changing the actual CSS layout of the site (which a developer needs to do for you)
Have you done any testing on internal pages for conversion? (hero image vs no hero image?)