following makes use of sstream. No need to create object on heap:

const char* what() const throw() {
    stringstream ss;
    string error;

    ss << n; //Integer passed to exception object

    error = ss.str();

    return(ss.c_str());  
}

This makes use of "c_str()" which converts your std::string to const char* (which is what c syntax for representing strings)