Power density characterization of battery systems reveals significant temperature dependence across operational ranges from -40°C to 60°C. This relationship stems from fundamental electrochemical kinetics, material property changes, and interfacial phenomena that collectively influence ion transport and charge transfer efficiency. The temperature-power correlation follows non-linear behavior with distinct regimes dominated by different limiting factors at extreme temperatures.

At subzero conditions, ionic conductivity in electrolytes decreases substantially due to increased viscosity and reduced carrier mobility. Below -20°C, most lithium-ion electrolytes exhibit conductivity drops exceeding 80% compared to room temperature values. This creates an Arrhenius-type relationship where power capability decays exponentially with decreasing temperature. The activation energy for this process typically falls between 0.3-0.5 eV for conventional carbonate-based electrolytes, resulting in a halving of available power for every 15-20°C reduction below 0°C.

Low-temperature operation introduces lithium plating risks during high-power demands. When charge transfer kinetics cannot keep pace with applied current, lithium ions preferentially deposit as metallic lithium rather than intercalating into anode materials. Plating onset occurs at lower C-rates as temperature decreases, with most graphite anodes showing plating below 0°C at rates exceeding 0.5C. This phenomenon creates irreversible capacity loss and safety concerns, effectively limiting practical power density in cold environments.

High-temperature regimes present different constraints. Above 40°C, solid electrolyte interphase (SEI) layers undergo accelerated growth and compositional changes. The increased ionic conductivity initially boosts power capability, but prolonged operation leads to SEI thickening that increases interfacial resistance. At 60°C, some lithium-ion systems show SEI growth rates 5-8 times faster than at 25°C, gradually degrading power performance despite the initial kinetic advantages.

Test methodologies employ environmental chambers with precision temperature control (±1°C) and multi-channel battery cyclers. Standard protocols include:
1. Hybrid Pulse Power Characterization (HPPC) tests at 10% state-of-charge intervals
2. Dynamic discharge profiles with stepped current demands
3. Electrochemical impedance spectroscopy at multiple temperature setpoints
4. Constant power discharge until voltage cutoff

Data collection focuses on three key metrics:
- Maximum sustainable power before voltage collapse
- Internal resistance calculated from current interrupt methods
- Charge transfer resistance derived from Nyquist plot analysis

Application-specific derating factors must account for operational requirements. Automotive systems typically derate power by:
- 40-50% at -20°C
- 20-30% at -10°C
- 10-15% at 0°C
- 5% at 50°C
- 15% at 60°C

These adjustments reflect both performance limitations and longevity considerations. The derating curves vary significantly by chemistry, with lithium iron phosphate (LFP) showing better high-temperature power retention but poorer low-temperature performance compared to nickel-manganese-cobalt (NMC) variants.

Material selection critically impacts temperature response. Electrolyte formulations with low freezing points and high boiling points extend the operational range. Additives like fluorinated carbonates can improve low-temperature conductivity by 20-30% while maintaining high-temperature stability. Electrode designs incorporating conductive networks help mitigate power loss at extremes, with some advanced architectures demonstrating less than 10% power variation between -30°C and 50°C.

The temperature-power relationship also shows hysteresis effects. Systems cooled from room temperature to -20°C may deliver 10-15% higher power than those equilibrated at -20°C for extended periods, due to residual thermal gradients and delayed phase changes in electrolyte components. This necessitates preconditioning protocols during testing to ensure representative measurements.

Accelerated aging studies reveal that temperature cycling induces different degradation modes than isothermal operation. Power capability decays faster in cells subjected to repeated -20°C to 60°C transitions compared to those held at constant elevated temperatures, suggesting mechanical stresses from material expansion/contraction contribute to performance loss.

Practical implications emerge for system design:
- Low-temperature applications require oversized cells to meet power demands
- High-temperature environments need careful thermal management to maintain SEI stability
- Hybrid systems combining batteries with capacitors can mitigate temperature limitations
- Pulse operation rather than sustained discharge improves low-temperature utilization

Advanced characterization techniques like in-situ neutron diffraction and atomic force microscopy have revealed nanoscale origins of temperature effects. At cryogenic temperatures, lithium-ion desolvation becomes rate-limiting, while at elevated temperatures, particle fracture from anisotropic expansion creates new surfaces that consume active lithium.

The comprehensive understanding of power density's temperature dependence enables optimized battery selection and operation across diverse environments. Continued material development and system engineering push the boundaries of temperature-resilient performance while maintaining safety and longevity requirements.