In my opinion, the heart rate monitor is useful in low or high temperatures, in particular.
I always thought that most of my progress comes from the winter running, but I couldn't explain why.
When the temperatures are very low, is easy to push myself, because the discomfort of body temperature is reduced. So I push myself at tempo and above level without being aware.
In contrast, when is hot, I tend to slow down, due to higher discomfort caused by temperature.
I found this recently, when I've compared the treadmill with outdoor, using a heart rate monitor.
On the treadmill the discomfort was higher, despite that I had 300 grams of gear and a faster pace at a low heart rate.
Outside the discomfort was really low, wearing 3-4 kg of gear, running slow at a high heart rate, even for longer time.