python threadsafe object cache
Well a lot of operations in Python are thread-safe by default, so a standard dictionary should be ok (at least in certain respects). This is mostly due to the GIL, which will help avoid some of the more serious threading issues.
There's a list here: http://coreygoldberg.blogspot.com/2008/09/python-thread-synchronization-and.html that might be useful.
Though atomic nature of those operation just means that you won't have an entirely inconsistent state if you have two threads accessing a dictionary at the same time. So you wouldn't have a corrupted value. However you would (as with most multi-threading programming) not be able to rely on the specific order of those atomic operations.
So to cut a long story short...
If you have fairly simple requirements and aren't to bothered about the ordering of what get written into the cache then you can use a dictionary and know that you'll always get a consistent/not-corrupted value (it just might be out of date).
If you want to ensure that things are a bit more consistent with regard to reading and writing then you might want to look at Django's local memory cache:
http://code.djangoproject.com/browser/django/trunk/django/core/cache/backends/locmem.py
Which uses a read/write lock for locking.
Thread per request is often a bad idea. If your server experiences huge spikes in load it will take the box to its knees. Consider using a thread pool that can grow to a limited size during peak usage and shrink to a smaller size when load is light.
You probably want to use memcached instead. It's very fast, very stable, very popular, has good python libraries, and will allow you to grow to a distributed cache should you need to: