Joule heating

Electric energy of both charging and discharging is converted into heat (i. e., warms the cell) at the rate (i. e., heating power) $I (U_{OCV} - U_{t})$, where $U_{OCV}$ is Cell open-circuit voltage and $U_{t}$ is Cell terminal voltage.

Another way to present the Joule heating rate is $I^2R$, where $R$ is the total cell resistance, i. e. a combination of Cell internal resistance and "diffusion resistance" (causing Cell diffusion voltage). However, this form of calculating Joule heating ignores the contribution of Cell voltage hysteresis.

The sum of Joule heating during both charge and discharge of the cell is proportional to the area between the charge and discharge cell terminal voltage curves plotted on the same chart, that's why Joule heating is called overvoltage loss in [2]:

Joule heating is also called irreversible resistive heating or simply irreversible heating in [5].

Reaction heating

The process of Lithium ions de-intercalating from the cathode and intercalating into anode when the cell is charged, or the reverse process when the cell is discharge can be exothermic or endothermic itself.

Reaction heat is also called reversible entropic heat in [1] (or simply entropic heat in [5]), and is governed by entropic potential (see the chart below).

Unlike Joule heating, which is always positive, reaction heating during charge is negative in the low state-of-charge range and is positive in the high state-of-charge range, and strictly reversed during discharge: positive in the low state-of-charge and negative in the high state-of-charge range (in an Lithium manganese oxide cell):

Picture from [1]

The negative reaction heating in the beginning of charge is higher than the Joule heating, therefore, a cell can slightly cool down in the beginning of charge at a low charging rate:

Picture from [3]. Battery surface temperature ("Can tempereature") vs. capacity during rate testing of the cells used in this study under charge (c) and discharge (d).

Heating in mixing process

When the cell is charged or discharged, especially at high currents, ion concentration becomes inhomogeneous, e. g. the electrode particles close to the separator are more (or less) lithiated than the electrode particles close to the current collector, due to gradients in current density. There are also area inhomogeneities (e. g. parts of the electrode closer to the current collector tab are lithiated differently than the parts of the electrode farther from the current collector tab, or on the edges of the roll) and Lithium ion concentration gradients within electrolyte.

When the current is turned off, these inhomogeneities spontaneously relax with a heating effect. In theory, this heating can be positive as well as negative.

Heating in mixing process (or heat of mixing) is a term from [1]. In [4], this source of heating is called entropic heat generation, which is very close to reversible entropic heat term used for reaction heat in [1]. Be careful not to confuse them!

[1] says that heating in mixing process is negligible, but [4] says that it could be 5-10% of the total heat losses in a cell. I think this discrepancy is due to the confusion in attribution of Cell diffusion voltage (which is caused by the ion concentration gradient within electrode particles) to either heating of mixing or Joule heating. [5] classifies the contribution of ion concentration gradients within electrode particles as a part of heating of mixing, and [4] may follow this classification. [1] apparently attributes cell diffusion resistance to Joule heating

Heating in side reactions

There are some side reactions in a cell when it's charged (Coulombic efficiency is never exactly 100%). If these side reactions are exothermic, this heats the cell. However, this source of heat losses in a cell is negligible.