If you see the HR climb during the run it means this run was conducted above your current Aerobic Capacity. So if you want that run to be an aerobic base building run you need to slow it down. Realize that aerobic threshold moves about from day to day. But, as a rule, you would want slow the pace during the run as you notice HR start to climb,
On hot days there is not as much blood available to carry oxygen to the muscle because more blood is being shunted to the skin for cooling. This causes the HR to rise for a given pace and the effort to feel harder. I am unsure of the metabolic affect this has but would suspect that you need to slow the pace accordingly is there is less O2 available for the work being done.