MacBook Pro overheating during large Pages file usage

I could do that hardware check, but the Genius Bar ran a full check, suggesting that it was a software problem.

EtreCheck excels at flagging, not "suggesting." software issues. In this setting whre we can neither see nor remotely access your device, it is the best tool we have for helping in this limited setting.

I am assuming that you do not experience overheating with other tasks. Correct?

You can limit how much Spotlight is indexing by doing System Settings > Spotlight. In Tahoe the "on/off' functions for what gets indexed looks like this:

By default, everything listed is checked. Some things tlike the App Store don't; need to be part of searches. Many Apple apps have built-in search, like Mail and Contacts.

This article amy also help: Rebuild the Spotlight index on your Mac - Apple Support

So I will re-phrase my question.

Is anyone experiencing extreme heating when using Pages in large files,

Perhaps your posting in the Pages forums section as well will help with that. More Pages users there:

Pages - Apple Community

It will help us get a good idea of what is causing your problem if you provide a report of your system, that way we do not have to play 20 questions with you. The report we are requesting does NOT provide any personal information and is extremely safe to use. Please navigate to www.Etrecheck.com and download the free version of EtreCheck. Once you have you downloaded the app and installed it, please run the report and save it. This report will help us get a good idea what has been installed on your system and help us be able to diagnose what may be wrong.

When you have your report, you can attach it when you reply to this message and we can then review it and help you determine what is needed to get your system running well again. 

For instructions on how to download your EtreCheck report and attach it to your reply to this message please click How to use the Add Text Feature When Post… - Apple Community It is helpful to us if you download the report to your Desktop.

Intel x86 processors including that I9 all run quite hot.

Mobile devices have lower cooling capabilities.

Kernel_task is throttling to reduce heat generation.

The Etrecheck data can show other issues. Common sources of issues include add-on anti-malware, add-on cleaner apps, add-on VPNs, and other such.

There can be many other issues arising here including broken apps, and insufficient main memory, too.

We can ask what amounts to thousands of questions (incrementally) and explain how to gather those details, or you can post the Etrecheck report.