I have had the same problem in the last week and have gotten in manny agruments at work about this question. Some people will say that it is a vital to the engine cooling properly as it holds the coolent in the radiator longer and alows it to cool properly, running the engine without the thermostat will make it over heat.
On the other hand, some people are telling me that I can run it without a thermostat and it will be fine, the only reason why you need one is to make the heater warm up quicker in winter...
I have searched these forums, as i assume you have, and there seems to be a few discussions about the tech sides of things IE: you will crack the head without running a thermostat, but either way I can't seen to find a straight answer either...
I have been running my standard 4k without a thermostat for about a week now and have done about an hour & a half straight and the temp has bearly moved, now that should be long enough for the engine to reach peak temp... I think ??
As for your thermo fan, my KE55 came with one aswell, and ocourse was wired up to IGN1 like yours... Personally i pissed the thermo fan of and put the original engine fan in .. Less wireing in the engine bay, the pulley for the fan is already there so why not take advantage of it ?
Sorry about the wall of text, lol >.<