The WISE article lists 22μm as its longest wavelength, though that might no longer be attainable since WISE is out of coolant. If one can find out what blackbody temperature has its peak at 22μm, then we could maybe see how close to the edge of WISE's temperature range the 400C (673K) and -10C (263K) dwarves are.
https://en.m.wikipedia.org/wiki/Wide-field_Infrared_Survey_E...
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Edit: found it: https://commons.m.wikimedia.org/wiki/File:Blackbody_peak_wav...
Looks like 20μm is a bit below 200K, so if I'm interpreting this right, WISE should have had no temperature-related problem (leaving aside brightness) spotting a -10C brown dwarf.
200 K is a bit below (water) freezing. 400 K is just over boiling. The 400 K object emits 16 times (2 ^ 4) more radiation than the same object at 200 K.