No an outboard doesn't have a thermostat, it's not a car. The problem is the impeller, it's worn out, replace it and all will be well.
You couldnt be more wrong. Most outboards have thermostats ive replaced several in diffrent size and manufactued outboards over the years. If your eska is like the other eska outboards I have seen than it is aircooled and overheating was a common problem.