Have you declared a BufferedReader in your class? If you make a class serializable, all the member variables need to be serializable as well unless you specifically mark them as not to be serialized, and BufferedReader isn't.
I'd also question why you'd want to serialize a Thread object, but maybe we should sort out this problem first.
What would it mean to serialize a thread? When you deserialize it, what do expect from it? To continue where it was when you serialized it? That's certainly not going to happen.
There are a few entities that are highly volatile - they only have meaning within the current JVM. Threads, input streams, output streams, connections - these are all things that should not be serialized.
If you want the thread's logic to be serialized, don't extend Thread but implement Runnable instead: