IEC recommends 30 degr. Cercius as a maximum temperature rise on a wire, under normal conditions.
You have a return of a total 2.7A. So the thinner wire that you can use is AWG24 (0.0511cm diameter) insulated straigt wire standing at free air.
Insulated AWG22 (0.003257 cm^2 cross section) will rise a temperature of 15 degr. Celcius @3A load under same conditions.
If you have to use a long wire, check the voltage drop as well.
to answer additional questions
IEE set maximum acceptable drop on conductors the 2,5% of the nominal input voltage.
In case of DC apply Ohm's law to calculate Voltage drop i.e. :
I is the total current of your load(s)
R is the total conductor resistance.
ρ= resitivity of the conductor. For copper at 25degr. Celcius is 0.023 Ωmm^2/m (or from manufacturers tables Ω/km for the specific AWG#)
L= the TOTAL length of the conductor in meters
A= the conductor cross section in mm^2
For AC some additional factors sould taking into account.
Having resistance and current, you can start calculating the power dissipation from conductor and using thermodymnamics to calculate temperature. There is a big difference between bare conductor (or PCB trace) and insulated one.
Common conductor (return) calculated using the sum of all currents.