The best DC chargers that are already out there are the 350kW chargers that the Ionity network have installed, so you can work out the potential charge times, at 5.83kWh per minute (enough to drive 20-25 miles).
The fat connection to the National Grid is where companies such as GridServ come in with their grid connected batteries & solar arrays, but as of now they have only one, http://www.gridserve.com/braintree-overview/
As for the heating up & cooling down of batteries for optimum charge rates, some Teslas already do this, & some other manufacturers have cooling. Then there are people like me who annoyingly “yo-yo” (speed up rapidly then allow the car to slow down, before doing it again & again) to warm batteries just before getting to a rapid charger so my batteries will take the maximum charge rate possible. The Pug e-2008 can technically warm & cool the batteries properly but it’s just not been implemented properly in the software yet, hence the yo-yoing fun & games, and the Pug doesn’t show brake lights when you take the foot off the accelerator as it doesn’t quite slow fast enough to trigger the european regulated regeneration braking requirement. (If you do this then make sure you have a dashcam facing rearwards to record the inevitable BMW as it crashes into your rear end).