How to make expectations on a mock object created inside the tested object?

I want to unit test a class that looks like this:

template <typename T>
class MyClass {
...
    void someMethod() {
        T object;
        object.doSomething();
    }
...
};

I want to unit test this class, so I create a mock class for T:

struct MockT {
...
    MOCK_METHOD(doSomething, 0, void());
...
};

Then I want to use it in a test case:

BOOST_AUTO_TEST_CASE(testSomeMethod) {
    MyClass<MockT> myClassUnderTest;
    MOCK_EXPECT(???)....;
    myClassUnderTest.someMethod();
}

How do I make an expectation for this object? My first idea was to store all created MockT instances in a static container from the constructor, then delete them from the container from the destructor. This would work if the object were created in a different method than where it is used, like this:

myClassUnderTest.createTheObject();
MOCK_EXPECT(MockT::findMyObject().doSomething);
myClassUnderTest.useTheObject();

But for this I would need to modify the interface of my class, and I really don't want to do that. Is there anything else I can do?