As transistor densities increase, power dissipation and operational temperatures rise, increasing economic and environmental costs. Asymmetric multicore processors (AMPs) have been developed to address this issue. These processors incorporate performance cores for demanding tasks and energy-efficient cores for lighter operations. They also utilize dynamic voltage and frequency scaling (DVFS) and uncore frequency scaling (UFS) to manage power consumption and temperature. However, process variations during manufacturing can lead to differences in power dissipation and maximum frequency capabilities among cores, impacting the processor's estimated lifetime and sustainable application execution. Hence, we (i) investigate the effects of process variability on the performance, power, and temperature of cores from an AMP system; (ii) study how they perform when subjected to distinct workloads and operating frequency settings; and (iii) identify optimal combinations of core mapping and operating frequencies considering process variability. Through an extensive set of experiments, we show that performance cores may have up to 5 times more power variability than efficiency cores. We also show that efficiency cores have more variability when executing memory-intensive applications, while performance cores are more susceptible to variability when executing CPU-intensive workloads.