Replace the water pump, even if it is new! The impeller may be slipping or have vanes broken and worn off. Some of these are pressed on and don't last very long.
I've had overheating problems. I had replaced the fuel pump a year earlier one Sunday in California while on vacation on the way to Sea World, as it gave up the ghost, steam rising, and it drained glycol out at the stoplight near the seashore. No Mechanics near or open, I walked until I found an auto parts store open and paid extra to have the pump delivered that day, so then we rented a car from a Fly-by-Night outfit nearby, and went to sea world for the day while the part was being delivered, and this is where the car alternator broke off. UGH and UGH again. The Maintenance crew was helpful as they had a metric bolt that fit, and with borrowed tools I remounted the alternator, got a jump and returned it to the idiot car rental, who would not send a wrecker or repairman. Boy, read the small print in the contract or you will pay for the tow. I replaced the water pump by flashlight in the dark of the parking lot with cheap Chinese tools I bought with the pump, bought just before they closed. My wife and daughter went to dinner while I drooled on the flashlight in my mouth.
Well, AGAIN I had overheating problems every time we went somewhere, in a stop and go or highway mode, you could watch the temperature rising. I replaced the thermostat, the sensors that are associated, that wasn't very convenient, and then scratched my head and decided to remove the pump expecting to find a stoppage somewhere. I could feel the bottom of the radiator was cool and the top very hot. It meant there was not adequate circulation. Upon removing the one year old water pump I found the impeller had come off and was spinning on occasion, when it felt like it I guess. A new water pump and the problem was solved.