Local potential competitor species are important determinants of the invasibility of an environment even when widely recognized invasive species are concerned since it may compromise its establishment. Thus, the outcome of the direct competition among the invasive khapra beetle, Trogoderma granarium, and the cosmopolitan species lesser grain borer, Rhyzopertha dominica and rice weevil, Sitophilus oryzae, and thus the likelihood of establishment of T. granarium under their co-occurrence, was here explored in paddy rice and wheat, at temperatures between 25 and 35°C and through 200 days of storage. Insect infestations were higher in wheat rather than in paddy rice. Trogoderma granarium was unable to displace any of the competing species under two and three-species competition experiments retaining lower adult population than both local competitors at the lowest temperature level. Rhyzopertha dominica prevailed in paddy rice, while S. oryzae prevailed in wheat. Paradoxically, T. granarium adults retained low population growth but contributed more for the total frass production and grain loss, much more than that recorded for R. dominica. Nonetheless, T. granarium larvae exhibited high population numbers 130 days after the introduction of the parental individuals. At higher temperature levels (30 and 35°C) the numbers of T. granarium larvae were extremely high even after 65 days, while the numbers of the other two species rapidly declined. Interestingly, the simultaneous presence of R. dominica and S. oryzae was beneficial for the population growth of T. granarium. Consequently, T. granarium has the ability to outperform other primary stored-product insects at high temperatures, while its presence at low temperatures remains for long periods apparently unaffected by other co-occurring species. Hence, T. granarium, in wheat, is able to outcompete other major species of stored-product insects at elevated temperatures, while at 25°C this species can maintain low numbers of individuals for long periods, which can rapidly produce population outbursts when the prevailing conditions are suitable for its development.