Polymorphism and overriding a method from a class template in C++

I would like to have a class template with basic implementations of my methods, and a set of subclasses that use the template class with particular types (double, int, char*) and override some subset of those base implementations, as needed. However, my overridden methods don't seem to get called unless I declare the object as an instance of the subclass. In exploring this problem I came up with the following code:

#include <iostream>

template <typename T>
class BaseClass {
public:
    virtual void print1 (T thing) {
        std::cout << "Base print1: " << thing << std::endl;
    }

    virtual void print2 (T thing) {
        std::cout << "Base print2: " << thing << std::endl;
    }
};

class IntClass : public BaseClass<int> {
public:
    void print2 (int thing) {
        std::cout << "Int print2: " << thing << std::endl;
    }
};

int main()
{
    BaseClass<int> thing = IntClass();
    thing.print1(1);
    thing.print2(1);

    IntClass thing2 = IntClass();
    thing2.print1(2);
    thing2.print2(2);

    return 0;
}

My expected output would be:

Base print1: 1
Int print2: 1
Base print1: 2
Int print2: 2

But instead, I get:

Base print1: 1
Base print2: 1
Base print1: 2
Int print2: 2

Is it possible to achieve my goal here, or am I better off creating separate base classes for each type in this case? Apologies if my terminology is a bit off - I am relatively new to C++.