From the docs:
tempdb is re-created every time SQL Server is started so that the
system always starts with a clean copy of the database. Temporary
tables and stored procedures are dropped automatically on disconnect,
and no connections are active when the system is shut down. Therefore,
there is never anything in tempdb to be saved from one session of SQL
Server to another. Backup and restore operations are not allowed on
tempdb.
This means that not only physical tables but also other objects like triggers, permissions, views, etc. will also be gone after a service restart. This is why you shouldn't use tempdb
for user objects.
You can create a schema in your own database and keep an SQL Agent Job that deletes all it's tables every once in a while, so you can mimic a "temporary" physical table space to work around.