if the water is fluctuating hot and cold then its nothing to do with the flow rate whatsoever.
it could be the hot water thermister but its more likely to be a blocked secondary or plate heat exchanger.
what happens is the dhw heat exchanger gets partially blocked with sludge, the water then passes through the heat exchanger a lot slower than normal so the water gets too hot, the boilers safey stats notice this and shut the burner down until the water cools, the burner then comes back on and the water gets too hot again, hence the hot water gets hot cold hot cold.
the soluton is a new secondary dhw heat exchnger as trying to clean them never really works. but if your central heating system is full of sludge then it may well block up again over time.