https://www.tegmart.com/thermoelectric-modules/18w-teg-module
These are rated for 626°F/330°C and intermittently up to 400 °C (752 °F)
A flat steel plate attached to the side of a cast iron stove could provide some cooling as you will loose heat/temperature with each layer you pass through. The heat flux is what you need to generate power, so you want your hot side near the maximum rated temperature and you want the cold side as cool as possible, you also don't want to heat or cool the TEG modules too fast. They are made of very brittle materials and rapid heating and cooling can cause them to fracture due to rapid thermal expansion. They really like to operate in a steady state environment.... You also want to be careful of your module to module connections as most lead solders melt around 400°F and will not hold up well in close proximity to the high temperatures.
The high end SiGe modules have been around since the 70s and have been used by NASA for decades. They can handle a much higher hot side temperatures (~1800F):
According to Wikipedia:
Application history[edit]
RTG Space Exploration Timeline
SiGe has been used as a material in RTGs since 1976. Each mission that has used RTG technology involves exploration of far-reaching regions of the solar system. The most recent mission,
New Horizons (2005), was originally set for a 3-year exploration, but was extended to 17 years.
Multi-hundred-watt (MHW) applications[edit]
Voyager 1 and
Voyager 2 spacecraft launched in August and September 1977 required
multi-hundred-watt (
MHW) RTG containing
plutonium oxide fuel spheres for an operational life appropriate for exploration of
Jupiter,
Saturn,
Uranus, and
Neptune.
[10] Conversion of the
decay heat of the plutonium to electrical power was accomplished through 312 silicon-germanium (SiGe) thermoelectric couples. A hot junction temperature of 1273
K (1832
°F) with a cold junction temperature of 573 K (572 °F) compose the temperature gradient in the thermoelectric couple in the RTG.
[10] This mechanism provided the total electrical power to operate the spacecraft's instruments, communications and other power demands. The RTG on
Voyager will produce adequate electrical power for spacecraft operation until about the year 2020.
[10] Similar MHW-RTG models are also used on the two U.S. Air Force communications
Lincoln Experimental Satellites 8 and 9 (
LES-8/9).
[11]