Airbox ducting?

Performance is of course one of the reasons, but keeping the carbs at the same pressure, and allowing an easy way to switch between cool air and under cowl air would be nice as well.  I've measured temps at the firewall just about 10" behind where one of the filters is, and it reads a pretty constant 140F in the 90+F summer heat.  That's about double the OAT at my cruising altitudes.  The last couple days it's been 70F in the afternoon, and climbing out gives easily 100 more RPM, so there's some low hanging fruit here, at least in the summer.   

I've read everything I can find on 912 carb ice, and opinions vary from don't need to must have.   I'll have some form of carb heat, hopefully just under cowl air.  I'm trying to find a reasonably priced used airbox to try, but the chances of it fitting are pretty slim.  Most likely I'd need to make a custom box. 

Rusty

Measuring the temperatures 10 inches from the air filter/inlets is not ideal - too far away.

Quite a few 912 powered aircraft have a NACA duct or similar, in the upper cowl. The idea is to  provide non directed air to the vicinity of the carburettor inlets. This could be a cheaper/easier option for you to try first.

As for "the carbs at the same pressure," as long as the float bowl breather tubes are correctly fitted this wont be an issue ie an air box is not required to obtain same pressures

Ideal of course would be to measure the temp inside the filter, and that IS possible.  Any other duct opening to the cowl would reduce cooling efficiency, since it would increase the pressure on the back side of the radiator/oil cooler.  It would be better if the cool air inlet was sealed to the carb or air box.  The cowl will be a works in progress for some time. 

Rusty

"Any other duct opening to the cowl would reduce cooling efficiency, since it would increase the pressure on the back side of the radiator/oil cooler. "

Not necessarily - I have seen several factory built aircraft move from a smooth no opening,  to various opening designs, on top cowl. All presumably to improve under cowl ventilation/cooling.

Much depends on your existing cowl design and the  location & size of coolant/oil cooling radiators.