>> the Gid meter shows that 30 kW power level heats the battery about 1 kW, and 40 kW heats the battery about 1.8 kW.
your heat loss estimates look a bit high: I'm getting about half that using 400V pack voltage and 100 mOhm internal resistance.
The battery impedance can vary, but I am confident that my calculation is reasonably close (+- 20%) because it is based upon the DC voltage drop I have observed under load with the Gid meter.
Since my post I realized we can calculate the worst-case temperature rise from battery discharge by neglecting all heat transfer out of the battery pack.
At 30 KW power level:, using my approximate measurement of 1% loss for each 10 kW:
(30 kW)*(1 % per 10 kW [measurement])*(30 kW) = 3% of 30 kW = .9 kWh per hour = .015 kWh per min
(.015 kWh per min)*(3,412 BTU/kWh) = 51 BTU/min
For a 650 lb battery pack, this yields (51/650) = .079 deg F per min, or 2.4 F
rise at 30 kW for 30 minutes.
At 50 kW power level, battery loss scales quadratically, so we have (50/30)^2 * 2.4 = 6.6 F
at 50 kW for 30 min.
The same process that causes the t^.5 loss of capacity also raises the battery impedance, so this heating will rise with age, but it should still not be a concern under most circumstances.
The graph I posted in another thread shows the impedance rising rather rapidly at very low SOC, so high power down here is not advised (and ultimately limited by the BMS). It also shows the charging process as being slightly endothermic at low SOC levels, and then becoming exothermic as the SOC level rises. This is consistent with the QC tapered charging profile.
The picture of the Tesla roadsters cooling off after short runs at high power was dramatic. The Tesla S is supposed to have more robust cooling of both its battery and motor.