Though, there was a random thing I would see in the logs where a random page would time out. It was very infrequent though.
I had it happen to me only twice in the past 3 years we've been here. (wow, I can't believe it's been that long!) When it happened to me, I got a blank page with no data. Just a white background.
I noticed that when I updated the version of Spring Boot I was using, the error basically disappeared. So that might have been the issue, or perhaps Heroku fixed something on their side around the same time. I also rewrote the thread tree building code at some point too that greatly decreased the amount of time the site was burning CPU cycles building the HTML... so I guess we'll never really know but I'm glad it seems like it hasn't been happening anymore.