Is there a small (watch or car alarm size) battery on the market that can withstand 400 deg F for 1-3 hours? If not, what would a higher temp battery specifications be?
Lithium Thionyl Chloride cells (3.67 Volt primary chemistry battery) in conventional AA form factor are available in retail packaging for low delivery rate applications (20-30 mA typical). Your preferred industrial supply vendor should be able to supply these as per regulations in your geography. These are sealed stainless steel and glass packages, designed for oil industry (downhole) sensors, among other things. Typical temperature ratings are 50 oC to 200 oC.
A somewhat lower cost substitute from Steatite in the UK is the Electrochem 4320, with the constraint that at temperatures lower than about 100 oC the battery capacity is very low, so as to be practically unusable at 10 mA load. If the temperature is guaranteed to be between 100 and 200 oC, this should work for you.
[Edit: I notice that the datasheet for these batteries rates them for operation from 70 oC, so it is possible that my recollection of minimum operating temperature is incorrect.]
Other options to consider include metal-junction thermoelectric power harvesting, if the power demand is very low. This would however require a cold junction somewhere close by, so it may not be a solution for your particular application.
From what I found from researching, there are batteries provided by Excell battery company that's able to withstand temperatures of up to 200 degrees Celsius (almost 204 in your case). However, these huge batteries are only available for industrial applications (Oil Industry, Medical Equipment, etc.). (Website link)
Although these batteries aren't able to withstand the temperatures you require, there are coin cell batteries from Panasonic that are able to withstand temperatures of up to 125 degrees Celsius. Luckily, these types of batteries could be purchased through distributors like Digikey and Newark for appx. $2 apiece. (Website link)
Hope this helps :)
Thirty years or so ago, there was talk of sodium-sulphur batteries which not only tolerated, but actually required, temperatures in that sort of range. I don't know their more recent history but it's a possible line of inquiry.