Should MySQL temp tables be indexed (or have a primary key)?

Should MySQL temp tables be indexed (or have a primary key)?

I am creating a stored procedure in MySQL which creates numerous temp
tables based on the data it processes.
After nearly completing the procedure I wondered...Do these temp tables
created on-the-fly really need an Unique key, Primary key, or Index?
The way I see it the data is not permanent so it's not necessary but maybe
it offers some sort of optimization?
Thank you in advance.