What is hot spotting in the context of adding files to tempdb?
What is hot spotting?

"Hot spotting" in this context means that, even though tempdb has multiple files, all the I/O work is being done in a single file. If tempdb is busy enough to justify adding files, the imbalance that leads to hot-spotting (due to proportional fill) will be short-lived, so I think the warnings may be a little Chicken Little. In my experience, anyway.
What about hot spotting makes things much worse in tempdb?

I think it is deemed to be worse in tempdb because it takes a brunt of the write activity in most workloads. You can certainly suffer similar problems in user databases, but since you're already trying to solve a problem in tempdb...
What specific things in the DB would get much worse?

Write times, mostly. Imagine everyone trying to use the same ATM, even when there are 7 other ATMs nearby. Only so much can be written at any point in time; everything else has to wait. With more files (and enough cores to schedule the work), the I/O can be spread more evenly.

Just make sure:


you have an even number of files
all the files are the same size
all the files have the same autogrow settings
the number of files is somehow driven by number of cores
depending on version (these are enabled by default in more modern versions of SQL Server), you are using trace flags 1117 (grow all data files at once) and 1118 (don't use mixed allocation extents).