What can cause a sudden rise in heart rate from 135 avg to 165 avg during 60 min run at same speed?

Heart rate: Just your heart responding to the continuing exercise

Atrial tachycardia: Paroxysmal atrial tachycardia is the most likely suspect for intermitent acceleration of heart rate during running at a fixed pace.

Increase in rate: Such an increase in rate could be caused by an episode of abnormal paroxsysmal tachycardia superimposed on the normal sinus tachycardia which is the rhythm occurring during vigorous exercise. Without a heart monitor recording your heart activity at that time, we can't be certain of the nature of the heart rhythm when your heart beat at 165/min. Apparently that very rapid heart rhythm resolved.

Other variables...: were all other variables held the same? incline, no consumption of food or drink?

Increased Work Deman: During a run, even though you are running at the same speed, if you change incline, terrain, or other factors this may increase your metabolic demand and even possibly your adrenalin level which could increase your heart rate. The normal response of the heart to increase work demands is an increased cardiac output and it does this in one way by increasing heart rate.

Physiology: Alhough you are running at same speed you are still running. I think this is a normal physiological effect. However, it could be that your running is causing some type of SVT.

..heart rate stayed-: 53 y/o Male asks What can cause a sudden rise in heart rate from 135 to 165 avg during 60 min run at same speed? One assumes there was no accompanying Shortness of Breath , Chest Pain/Exhaustion. Also that there was no mechanical error by the machine. One needs also to know how long after said exercise the heart rate stayed elevated. A visit to PCP/Cardiologist might help ensure Good heart health