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As popular as the Rotax engines are, I would think there would be a TOCA (thermostatic oil cooler adapter) available for the 912. I've got one on my Jabiru 3300 and it greatly reduces the warm-up time in the winter. Since it is thermostatically controlled, you don't need any doors or flaps to regulate the oil temp - it's automatic!
I tried the oil cooler door / flap.... not so much luck.
I used 3 strips of duct tape over the oil cooler NACA duct 3 winters with reasonable success.