The way to efficiently operate some power devices with less loss, and appropriate heat sharing
You could calculate the dissipation of your application and compare it to the Temperature Derating Curves.

The last derating curve example is 12V in, 1V 10A out. From the Efficiency vs. Line Voltage graphs, I estimate an efficiency of 78% at conditions 12V in, 1V 10A.

Defining Ploss the power dissipagtion that causes the converter to heat up:

Ploss = Pin - Pout 

Efficiency = Pout/Pin

Ploss = Pout/Efficiency - Pout

Ploss = (1V*10A)/0.78 - (1V*10A) = 2.82W

From the Efficiency vs. Line Voltage graphs, you could estimate the efficiency using your output voltage and current. And next, calculate the power dissipation. 

If it is below 2.82W you can use the converter up to about 38 degrees C using no fan (nor heatsink, where would it be placed??) and need to derate according the last graph of the Temperature Derating Curves.

I didn't address your original question yet if it would make sense using a shottky to lower the input voltage.
I think it would make sense, if you exceed the 2.82W above.
The Efficiency vs. Line Voltage graphs show that a lower input voltage gives a higher efficiency, and so, less dissipation.
Note that a standard diode would even better in this case than a schottky diode.