What special measures do I have to take to commute in frigid temperatures?
First of all, I haven’t done anything as extreme as you, only -18°C.

The bike should be fine, maybe use less viscous chain oil and grease. I’ve ridden normal (though quite supple) Michelin Mud2 and Schwalbe Racing Ralph cyclocross tires in -10°C and didn’t notice any difference in their performance. In even colder weather I’ve only ridden studded Nokkian tires. There are special winter tires, e.g. the Conti Top Contact Winter 2 which might be a good idea in any case.

Be aware that cables can freeze and molten snow can form ice on your rims. Regularly check that you are still able to brake, especially before approaching an intersection or the like. Battery powered lights might run into problems (or at least reduced battery run-time).

Regarding clothing: Think about all the contact points between you and the bicycle: Saddle, pedals and handlebar (brakes, shifters). If you can comfortably sit in the saddle with your -40°C winter pants, don’t rub on the crank arms with your -40°C boots and can still shift and brake with your -40°C gloves everything should be fine. For your hands you could get Bar Mitts which allow you to wear thinner gloves. This assumes that your clothing is otherwise suitable for wind and strenuous activity in the cold weather.