Clean way to turn interrupts on and off?

The timer interrupt is slow (1s) to service a temperature control loop, and the external is a once-around pulse on a slow running motor (~3.5Hz).
I need to turn off the temperature control loop from time to time to act on some motor events.
And I'll ultimately need to turn of the external motor interrupt when I add a faster timer interrupt (say 125us) to sample some data.

That makes zero sense.

There must be a slick way to turn interrupts on and off individually with minimal avr register writes. Or something.

Yes, there is - all outlined in the datasheet.