Heat maps will definitely help you fix issues or make quick changes. But when you need a more in-depth understanding of how to improve the user experience, you'll get more out of heat maps by combining them with other behavior and feedback tools.
Heat maps + traditional analytics
With traditional analytics like Google Analytics, you'll get plenty of quantitative data points and learn about large-scale traffic and usage patterns---but numbers and charts will not, by themselves, answer questions you might have about what people want from your site, where they get confused, and where their attention goes.
By combining traditional analytics with heat maps, you can start a deeper investigation and find out why some of your metrics occur. Got a page with lots of traffic that doesn't convert? Set up a heat map, go through the heatmaps analysis checklist, and start seeing what's making people stumble.
Heat maps + A/B testing
As a visual tool, heat maps help you make informed, data-based decisions for A/B testing, updating, or (re)designing your website.
Both are so interlinked: you can use heat map data to define a hypothesis for a future split test, and you can also run heat maps on A/B test variations to provide more insight into why page versions are or aren't successful.
The idea is to create different versions of your web pages, ads, landing pages, etc. in order to compare how they perform.
Heat maps + session recordings
While heat maps help you visualize data from page visitors in aggregate, session recordings are created for individual users and show you their actions across multiple pages.
Session recordings are renderings of user browsing sessions, and they help you bring more clarity to some of the insights you pick up from a heat map. Instead of making assumptions about the clicking, tapping, and/or scrolling you see on a heatmap, try viewing some session replays and see how your users actually interact with your site.
Heat maps + on-page feedback
Use heatmaps to find design issues and other glitches and ask your users for feedback to improve the user experience.