These are good observations. The Tesla Battery comes in 65 kWh and 85 kWh. Lets assume that we are talking about the 65 kWh battery (which makes things look worse from the heat dissipation side)
According to your numbers, 150kW delivered for 40 mins = 100kWh so 35kWh of energy must be dissipated during charging.. Ouch! if this is an 85kWh battery than its only 15kWh which you can start to imagine in terms of 10+ Hair Driers, not so bad, but significant.
This is the part where they partially address this...
It has an energy efficiency (defined by IBM as “the ratio of the energy to discharge the battery over the energy to charge the battery”) of over 90%.
This means heat loss on both charging and discharging is combined to less than 10% Lets assume 5% each way. This would be one third of the heat loss required for the Tesla if this is an 85kWh model’s charge time, or one seventh of the loss for the 65kWh model if that is what these numbers represent.
So, we go back through the numbers. 480V is max available for most situations so this is going to be fixed, and frankly 480V is pretty dangerous regardless.
Still at 480V, if I haven’t screwed this up @ 95% efficiency you would need 1,625 Amps to push 68kWh into an 85kWh battery. (this is the 80% charge time) - It would require some sort of drive up Bus Bars that slide into notches under the car. A cable that would carry 600 Amps at 480V more than 2” in diameter. It would take 3 - 1x6 Copper bars to carry this current.. LOL.
Perhaps there is a patent here.. if one decided to pursue it.
480V is not dangerous it is used everyday in thousands of industrial warehouses as 3 phase 480V AC power I personally have plugged with my bare hands into a live 480V socket a 50kw motor its no more dangerous than plugging in a 120V appliance as long as common sense is used. This is besides the point the current supercharger standards all have dead plugs and terminals until a complex handshake and charge communication protocol has been negotiated between the vehicle and the charge station the user is never exposed to live current at the plug nor cable.
The current standardized Type 2 plug has 8mm DC pins and 6mm AC pins for THREE PHASE power at up to a standard of 600V and 160 amp on EACH OF THREE PHASES. 160x3x600 = 288000 watts or 280kw. The current model 3 Tesla can take up to 250kw level 3 supercharger rates as designed from the factory. 480V 3phase AC power is the backbone of light industrial power in the north American market it is available anywhere you have industrial AC power think every warehouse and light manufacturing plant or shopping mall. In Canada the standard is 600V. Put in realistic terms 480V 160amp 3 phase is 230kw of power and this is available nearly everywhere you have commercial power services.
The Type 2 standardized plug also accepts 250amps at up to a now standardized 1000V DC for a 250kw DC fast charge. Three phase moderate voltage AC charging is the future, google ChargeAll for what the future of EV architecture looks like. Steping up too 960V 3 phase is harder to come by but is used for heavy industry so the transformers are readily available. 960V at the same 160 amps in 3phase AC power is 460kw.
Given that most local power pole voltages are 15000 volt three phase AC the source of 960V 3 phase is already in the neighborhood. also given the standard allows a max 1000V DC over the type 2 plug architecture means 960V 3phase AC is an afterthought from a materials stand point.
As for heat dissipation battery packs are now all liquid cooled with the same ethylene glycol antifreeze that cools gasoline engines. Put into perspective a 180hp gasoline engine is dissipating 75% of its net output in heat 25% at most is output to the wheels sorry thats just thermal dynamics. This is a simple calculation a vehicle getting 30mpg is using 4133 btu per mile in chemical energy 124000btu/gal of E0 / 30 = 4133btu/mile there is 3412 btu in one kilowatt hour so that vehicle is using 1.21 kwh in raw chemical energy per mile traveled.
A Model 3 Tesla uses 230 watt hours to go the same distance this gives you an idea on how much actual energy it takes to move mass down the road as batteries are 90+ efficient as are electric drive trains. For simplicity 230/1211= .1899 or 18% gasoline efficiency vs electricity. Why go through this calculation? My ICE car avg 30mpg and weights less than a model 3 has comparable seating and trunk space so comparable frontal area and therefore aerodynamic drag,less mass moving down the road which by physics takes less energy to move less mass a given distance with similar aerodynamic drag.
The heat dissipation system in my ICE is capable of removing a net of 180hp worth of heat given that to get 180hp net you have to burn 720hp worth of heat energy again only 25% of gross makes it at best to the wheels. In a ICE motor half the heat goes out the exhaust system we will be generous and say 60% the rest is deposited into the oil and coolant systems. So 720hp gross chemical energy x .75 x .40 enters the coolant system at its max design point. Thats 216hp worth of heat into the coolant system 216hp x 745.7 watts to the hp = 161000 watts dissipation in the radiators.
Charging a 90% efficient round trip battery means 5 percent is lost to heat each way so 5 percent of 250kw charge rate is 250,000 watts x 0.05 = 12500 watts of heat not even a tenth of the heat dissipation of a typical electric fan cooled radiator under virtually every hood in America. This is why the Model 3 can charge at up to 250kw with a liquid cooled pack heat is a non sequitur.