Steady state training means steady HR, right? Wrong!
Your HR will increase due to a condition called cardiac drift.
Let’s say you run for an hour at a certain pace. Throughout that hour your body temperature rises, you start sweating, and lose some fluids. The fluid loss actually comes from your blood stream; so, the blood is redistributed in your body, blood volume decreases, which in turn decreases stroke volume. Your increased HR is to help compensate for lower stroke volume and to maintain a constant cardiac output.
In short, while your speed per km(or mile) can stay the same for the entire hour run, your HR will increase! Have fun!