Text classification into thousands of classes
In general this doesn't work well, since it's almost unavoidable that the classifier won't be able to distinguish all the categories from each other. I'd suggest tying to reduce the number of categories (for instance discard the least common ones). 

In any case I'm not aware of any specific model to deal with a high number of classes, it's regular text classification. I'd suggest to start with a robust method such as decision trees, but there are many options.