How do I put a thread in a C++ smart pointer?

You can put std::threads where ever you want, they are not special. Destroying thread handles is problematic. You can implicitly detach, implicitly kill or implicitly join and every option is bad. std::~thread (usually) just kills the whole program. To prevent that join or detach it.
Since you seem to want to implicitly join you may want to use std::async (probably with the std::launch::async policy) to launch your threads. It returns an std::future who's destructor implicitly joins.

it's possible to create std::unique_ptr<std::thread>. It will call std::thread destructor, when scope of unique_ptr will end. Remember that calling std::thread destructor is not terminating running thready gently, but by std::terminate. To end std::thread normally, you have to run .join() on std::thread object.

According to cppreference.com,

A thread object does not have an associated thread (and is safe to destroy) after

• it was default-constructed
• it was moved from
• join() has been called
• detach() has been called

So if you define the thread as a member variable and write your destructor like this:

~my_class(){    done_ = true;    my_thread_.join();}

everything is fine, because it is guaranteed by the standard that the std::thread destructor will be called only after the my_class destructor, see this Q/A.