Your thermostat is the Permacool. I have the same on the autogyro I just bought and like you it takes a long time to heat up the oil on a cold day. You are obviously in a country where it gets very cold so, in winter, you could probably change the internal "waxstat" to a MotoRad P7200-195. as described by Denis without any risk. You could probably go to a 205°F stat without much risk either, it's your call.
It's normal that your friend's engine, with water thermostat, warms up quicker. With the thermostat in the cold/by-pass position there is very little water in the circuit that is essentially the 4 cylinder heads and a bit of 1" pipe. That water will heat up quickly and heat the oil that lubricates the rockers quickly. Sorry if you already know all this.
I'm not sure I agree with your comment that a water thermostat is safer than a heat exchanger. It's difficult to compare the two. A thermostat only introduces 3 or 4 extra water connections that could leak but is still a cheap mass produced (but where and with what quality control????) item most of which fail in the bad position for the pilot and the engine.
The heat exchanger probably requires a lot more plumbing and extra connections that could leak but is usually a better manufactured item that has no working/moving parts so, in theory, is less prone to failure than a cheapo thermostat.
That being said we are not hearing horror stories of aircraft falling out of the skys due to thermostat or heat exchanger failures so maybe we're all being over cautious.
It's a choice only each owner/pilot can make, if you're not happy with your own engineering skills to make the decision don't do it.
Mike
