Ambient temperature control

Assuming you can keep a device in its "normal operating (temperature)
range", how advantageous is it (think MTBF) to drive that ambient
down?  And, is there a sweet spot (as there is a cost to lowering the
temperature)?
Also, is there any advantage to minimizing the hysteresis between
the ACTUAL operating temperature extremes in such a control strategy
(given that lower hysteresis usually comes at an increased cost)?