DBCC checkdb on tempdb
No, it's not recommended because it's largely a waste of time. When SQL Server restarts, tempdb is created from scratch. Also, the data in there isn't around long enough to be a good indicator of if there's an issue with it, or the underlying storage.

Both Ola's scripts and Maintenance Plans will skip tempdb when you set up CHECKDB routines.

Another reason why it's largely useless is because if tempdb does get corrupted, you'll know in a hurry. Check out my blog post here where I corrupt tempdb on purpose: DBA Days: Killing TempDB softly

Coming up in SQL Server 2019, we'll be able to use "in memory" technology for system tables in tempdb. While this solves pretty big contention issues, you can't run CHECKDB against in-memory tables. The only way you could check those is if you backed up tempdb, which isn't something you can do.

BACKUP DATABASE tempdb TO DISK = 'D:\Backups\t.bak'



  Msg 3147, Level 16, State 3, Line 27 Backup and restore operations are
  not allowed on database tempdb. Msg 3013, Level 16, State 1, Line 27
  BACKUP DATABASE is terminating abnormally.


If you really think it's worth running checkdb against a database that SQL Server won't allow you to back up, well, it's your maintenance window, I suppose.