I have never flown B737, but if I'm understanding the question correctly the FMC gets it the same way a human would.
1) You go to the MAX N1 (bleeds on/off table) SETTINGS Table.
2) Put OAT or in your case you use the "Assumed Temp" as your OAT.
3) Find the MAX N1 allowable for that temp. So if it's an Assumed Temp you use that temp.
Now, how do you find what's the maximum assumed temp you can do.
You basically have to reverse walk on a Runway limit and Climb limit graph, or airport analysis table as they like to call them these days.
You find your weight maybe add a couple hundered or thousand pounds to allow for some leeway (depending on airplane size). Then trace backwards on the graph or table to account for runway length, pressure altitude and so forth and find out what's the maximum temprature you could be assured of that your airplane will not be limited at your takeoff weight. You use that temp as your assumed temp.
TIP:
If you can get your hands on Section 5 & 6 of some old 737 classic, or 747-100/200 or some 757-200 books from Boeing. They should contain all the graphs (notice I wrote GRAPHS) of Runway limit, climb limits etc. If you trace your finger to figure out the limits everything becomes clear.