A capping inversion can be the difference between a thunderstorm event and no thunderstorms developing. If the air is too warm aloft then rising parcels of air from the surface will be cooler than this warm air aloft. This will cause the parcels to sink back to the surface. This sinking represents a stable situation.
This layer of warm air aloft is refereed to as the cap, lid or elevated mixed layer. There is a handy rule of thumb in operational meteorology for determining if the cap is strong enough to likely prevent thunderstorms from developing. This rule works for non-mountainous regions in the warm season. If the 700 mb temperature is warmer than 12 C then it is likely that thunderstorms will not occur unless some mechanism or process cools this temperature. Processes that can cool this temperature include dynamic lifting (i.e. frontal lifting, PVA). If no lifting mechanisms are present then daytime heating will likely not be enough to initiate thunderstorm development if the 700 mb temperature is higher than 12 C.
In the next thunderstorm situations coming up, check the 700 mb temperature and see how well this rule of thumb works.