Hi John,
While CHECKDB process is running, SQL Server keeps the information about the scanned portion of DB. This is to compare the information at one point with another point. SQL Server keeps these information in the memory in worktables. So if memory reaches its limit, these information will spill out to tempdb causing the tempdb to grow.
You can estimate how much space tempdb will take for the CHECKDB operation of a database.
DBCC CHECKDB WITH ESTIMATEONLY
This code will only estimate.
Thanks