Site-specific on-demand cooling of hot spots in microprocessors can reduce peak temperature and achieve a more uniform thermal profile on chip, thereby improve chip performance and increase the processor’s life time. An array of thermoelectric coolers (TECs) integrated inside an electronic package has the potential to provide such efficient cooling of hot spots on chip. This paper analyzes the potential of using multiple TECs for hot spot cooling to obtain favorable thermal profile on chip in an energy efficient way. Our computational analysis of an electronic package with multiple TECs shows a strong conductive coupling among active TECs during steady-state operation. Transient operation of TECs is capable of driving cold-side temperatures below steady-state values. Our analysis on TEC arrays using current pulses shows that the effect of TEC coupling on transient cooling is weak. Various pulse profiles have been studied to illustrate the effect of shape of current pulse on the operation of TECs considering crucial parameters such as total energy consumed in TECs peak temperature on the chip, temperature overshoot at the hot spot and settling time during pulsed cooling of hot spots. The square root pulse profile is found to be the most effective with maximum cooling and at half the energy expenditure in comparison to a constant current pulse. We analyze the operation of multiple TECs for cooling spatiotemporally varying hot spots. The analysis shows that the transient cooling using high amplitude current pulses is beneficial for short term infrequent hot spots, but high amplitude current pulse cannot be used for very frequent or long lasting hot spots.