Making Hot and Cold room at the same time with Peltier stack
In my limited experience, 140C is far too much temperature difference for typical Peltier stack. (My experience is limited to building a demonstration board for our own in-house training, using our own (Maxim Integrated) MAX1968/MAX1969 TEC regulator IC. I used a single TEC element with a simple heatsink + fan IC cooler arrangement, and did not address regulating a temperature chamber.) It might be possible with careful component selection and design attention to insulating the hot and cold chambers.

Study the datasheets carefully, for example CUI Inc CP85, the CP85438 is rated 15.4V 8.5A best case deltaT max 75C (measured in a vacuum). But the real story is found in the typical performance chart:



This chart shows a family of curves representing the typical achievable temperature difference, as a function of drive current. At 1.7A, the temperature difference is about delta-T=35C when no heat is being pumped, but drops to delta-T=0C (no heat flow) when 20W is being pumped. At the maximum rated 8.5A drive current, a temperature difference of over delta-T=70C is possible as long as there is little or no heat transfer. At 8.5A this part is capable of pumping a maximum of just over 80W of heat. This is what limits the performance of this component. Also note how close the 6.8A and 8.5A lines are, there is diminishing returns from increasing the drive current.

It is also important to realize that as soon as drive current is removed, heat begins flowing back across the junction, to equalize the hot and cold side. So when the device is powered off, the cold side may feel a sudden temperature increase.