I agree with Frankieboy. Check also your strainer basket. Mine is normally pretty clean after a year but this year, after a circumnavigation of Britain, it was completely clogged when I checked a week ago. I think it is almost certainly poor flow of raw water; I had this for years with my boat and it persisted after completely stripping down the heat exchanger (very little crud after 18 years), replacing the exhaust elbow, replacing the strainer basket, replacing the impeller and seawater pump cover. It turned out in the end to be a very worn cam in the seawater pump. Changed that in a few minutes and now the flow is much greater and it always starts without delay.
I don’t have an exhaust temp gauge so I don’t know where your sensor is but I suppose there is a very, very remote possibility of the exhaust water lock being blocked somehow. I’d look at the obvious things above first.