For attaching ZX Spectrum 128K to SD card storage, WiFi and PC please consult ZX Spectrum 48 page.
The big radiator which distinguishes 128K from its predecessors is attached to a popular 7805 voltage regulator used to reduce 9V from the power supply to 5V needed by the electronics. This regulator can fail often, for example when you mix the polarity of the power supply, but it is easily replaceable with a new part.
Power supply is 9V DC with ground in the center. This is similar as in case of ZX Spectrum+ and ZX Spectrum 48, but the one I have with 128K is rated at 1.85A. Not sure if this is really needed though.