Safety pilot reported the pilot flying had a runway excursion during landing followed by impact with a runway light. Safety pilot took control of aircraft and recovered on side of runway.

Narrative

Aircraft X was involved in a runway incursion during which hit a runway light on the left side of Runway XX. I was scheduled to do a rental check out flight with Person A. We took off on Runway XX and went out to the north practice area to do maneuvers. Once maneuvers were finished; we headed back to ZZZ to do 3 touch and goes. The PIC decided to do a straight in approach for Runway XX; we proceeded to land on Runway XX. Then PIC applies full power; without having cleaned up; flaps were approximately between 25-30 degrees and the carb heat was still on. After I see this; I immediately say; 'my controls' and 'power idle' (I say these phrases 2-3 more times before PIC finally relinquishes the controls) but by that time the PIC had panicked and gotten us into a left skid across the runway. I immediately pull throttle to idle and correct the left skid with right rudder but by that time it is too late; and I recovered the aircraft at the side of the runway. And then proceeded to hit a runway light with the tire strut. It is important to note I acted as a safety pilot for a rental checkout flight for the PIC; I would only take the controls if I saw a hazardous scenario about to incur.I believe that I took evasive actions to avoid an even more precarious situation. PIC did two things that are against POH guidelines. 1. Taking off with more than 10 degrees of flaps; (PIC had 25-30 degrees of flaps). 2. PIC did not turn the carb heat off before taking off; (PIC had carb heat on)3. The third factor that led to my decision was the weather. At the time of the incident the temperature at ZZZ was 32 degrees C and the density altitude was 3000ft.All three of these factors reduces the aircrafts climb performance; and at which point I felt that I had to take the controls; due to us being already halfway down the runway. What caused the accident? Once I said; 'My controls.' The PIC seemed to freeze and kept his hand on the throttle at full until the aircraft got into the left skid across the runway. Then he relinquished his hand off of the throttle and allowed me to reduce it to idle and then applied right rudder to stop us from going off the side of the runway. If my corrective action was not taken at the end the aircraft would have almost definitely been off the runway and into a ditch.