are its local (my) variables in global storage or thread storage?

My first reaction to this is: Why do you want to know?

But since such meta-questions can be really annoying, I'll expand a little :)

Pretty much everything user accessible in Perl is allocated from the process heap. That said, there is a complication in that the heap is broken up into buckets and some buckets can be reserved for use by particular threads.

The important thing about about variables in threaded programs, is not where the storage is allocated. It is their visibility.

A secondary consideration is whether they are cloned, but that's a complex issue that would require a lot of words to describe. And someone intimately familar with Perl's internals to both describe, and subsequently understand the description.

Which brings us back to my initial reaction above. If you explain why you want (or think you need?) to know, then you're more likely to get a reply that will be useful to you.