Turnigy nanotech 35C/70C 4S lipo, I can build down to .1 at full power and JUST be hitting the pulse limit of the cell. I have MaxxAmps that can handle 100C loads. All depends on the battery. By thousands I literally mean 1,000-5,000W. I never personally exceed 1,200W and that's RARE when I even go above 500W. I just like lipo PWMs.
As far as 3,500W and above, you'd need a 5-6S lipo (which my mod will take, any cell 2S-6S is compatible) to do that or a REALLY nice 100C 3,000mah+ 4S. 6S Lipo PWM at full charge/full power would put out around 25V, get a 0.065 build, boom 10,000W. Yeah it requires around 400A, but lipos (Especially when you get into 6S+ ones) can very much handle that if you get a larger, nicer one.
I made this box myself and use it every day.
Specs:
CNC Alpinetech ATI 1590N1 style hidden magnet/no lean enclosure w/ .28 meter cutout.
Big Al IntelliPWM 2S-6S Smart PWM board with potentiometer installed (with bezel).
Magnetic (Neo) door.
2,200mah 16.8V 4S Turnigy Nanotech 35C-70C lipo.
30mm smooth top Varitube 510
12 gauge silicon copper wire for all load bearing connections, 28 gauge stranded copper for switch/meter connections.
12mm horn-style dual post antivandal switch
XT60 connector
.28 SMAKN green volt meter.