How about this as a suggestion. The water with an unknown temperature above 40 degrees must be cooler than 100 degrees (boiling point) right? So if you take 100 ml of that water (x degrees) and mix it with 200 ml of ice cold water (zero degrees) the new temperature will be equal to (0 + 0 + x)/3 or simply x/3. Now since the hottest x can be is 100 degrees, the hottest x/3 can be is 33.3 degrees, which you can measure with your 40 degree thermometer.
So for example if the unknown hot water is at 60 degrees and you mix 100 ml of that with 200 ml of ice cold water, the new temperature will be 20 degrees. to get back to your unknown you just multiply by three.
You follow?