The thermodynamics of the ocean and atmosphere partly determine variability in tropical cyclone (TC) number and intensity and are readily accessible from climate model output, but an accurate description of TC variability requires much higher spatial and temporal resolution than the models used in the GeoMIP (Geoengineering Model Intercomparison Project) experiments provide. The genesis potential index (GPI) and ventilation index (VI) are combinations of dynamic and thermodynamic variables that provide proxies for TC activity under different climate states. Here we use five CMIP5 models that have run the RCP4.5 experiment and the GeoMIP stratospheric aerosol injection (SAI) G4 experiment to calculate the two TC indices over the 2020 to 2069 period across the six ocean basins that generate TCs. GPI is consistently and significantly lower under G4 than RCP4.5 in five out of six ocean basins, but it increases under G4 in the South Pacific. The models project potential intensity and relative humidity to be the dominant variables affecting GPI. Changes in vertical wind shear are significant, but it is correlated with relative humidity, though with different relations across both models and ocean basins. We find that tropopause temperature is not a useful addition to sea surface temperature (SST) in projecting TC genesis, perhaps because the earth system models (ESMs) vary in their simulation of the various upper-tropospheric changes induced by the aerosol injection.