I was thinking about doing this to my 35 when I put temperature speed controller on the fan (oh the blessed sound of silence), but did not, I had power supply that fitted but was worried about heat and dust or liquid if I'd cut cooling holes.
Basically you need Switch Mode Power Supply that supplies 13.8 volts and 20% more amps than you charge with, 8 amps is pretty common SMPS size and should work perfectly for this application. Power supply from old computer might work. They´re usually 12 amps or more, but have 12 volts which may not be enough.
Switch Mode Power Supply 12V
Switch Mode Power Supply 15V
At 169X98X38 millimeters both should fit and they have voltage adjustment for fine-tuning. I don't remember if the 35 is ok with 15 Volts.