The growth of renewable energy requires flexible, low-cost and efficient electrical storage to balance the mismatch between energy supply and demand. Pumped thermal energy storage (PTES or Carnot battery) converts electric energy to thermal energy with a heat pump (or another heating system) when electricity production is greater than demand; when electricity demand outstrips production the PTES generates power from two thermal storage reservoirs (possibly a Rankine cycle mode). Classical PTES architectures do not achieve more than 60% roundtrip electric efficiency. However, innovative architectures, using waste heat recovery (thermally integrated PTES) are able to reach electrical power production of the power cycle larger than the electrical power consumption of the heat pump, increasing the value of the technology. In this paper, a general model is developed to draw mappings of performance depending on the two main inputs (waste heat and ambient air temperatures). Whatever the storage configurations, the best performances are reached when the waste heat temperature is high, the air temperature is low, and the lift of the heat pump is low. Finally, the thermally integrated PTES technology is compared with other technologies of energy storages and is theoretically promising due to its high roundtrip efficiency, its low specific price and no specific geographical conditions.