Thermal inversions have become the standard instrument for estimating the causal effect of air pollution, underpinning at least 81 published studies of health, labor, firm, and crime outcomes. Seventy-seven percent of those studies concern China, and none concerns Sub-Saharan Africa. This paper examines whether the design can be transported to the regions where pollution research is expanding fastest. We link 120,820 children in 26 Sub-Saharan African countries and 128,919 in India, Bangladesh, and Nepal to 0.01° satellite PM2.5 and to ERA5 temperature profiles measured at local dawn, and we estimate a single two-stage least squares specification six times, changing only the definition of the inversion instrument. Five of the six definitions come from published practice, and the sixth is an elevation-robust variant of our own. In the African sample, we find that all six first stages are strong and correctly signed (F=57-356). However, the second stages split by instrument family. Pressure-level definitions give positive but insignificant effects on child respiratory illness, whereas surface-layer definitions, the modal implementation in the literature, give significant negative ones. Over-identification tests reject the cross-family pairings of the count and continuous instruments (p<10^(-4) by the Sargan statistic and p≤0.002 with cluster-robust weighting) while accepting every pairing within the pressure-level family. In addition, the surface-layer family fails a diarrhea placebo test. In India, two instruments built from the identical temperature difference, differing only in functional form, have opposite-signed first and second stages. In Bangladesh, where the terrain is at sea level, pollution is extreme, and winter inversions are severe, all six first stages are significantly negative because inversions peak in March while transport-driven pollution peaks in January. These failures appear to be structural. An inversion day moves measured monthly PM2.5 by roughly one microgram per cubic meter, so large F statistics can coexist with an experiment too small to dominate the direct health effects of the accompanying weather. Moreover, the conditions that strengthen the first stage are the same conditions that open those direct channels. Validation against ground monitors further suggests that the fine-scale exposure contrasts many of these designs rely on are largely absent from the satellite data. We provide a nine-item diagnostic protocol and apply it to 26 applications coded in full text. None satisfies more than three of the first eight items, while the two seed papers satisfy six. The seed papers also used different definitions (balloon-sounding profiles in Arceo et al., the 1000/925 hPa pressure difference in Jans et al.), and their instruments moved exposure by 3.4 to 25 percent of its mean, compared with 0.01 to 0.07 percent in the citing studies that report comparable magnitudes. In our data, the seed papers' pressure-level definition behaves coherently, whereas the unvalidated surface-layer definition fails.