as far as i am aware, the sensors draw betwee 2 and 4 amps during heating, and then 1 amp continouous when hot.
I ran mine off a relay triggered by Fuel pump power, which was controlled by ECU.

is it 3 wire, or 4 wire? if it had 3 wires plus sheath, then it is just a 3wire....

the integrated sheath is usually just a noise shield, similar to what is used for CAS and other sensors, to protect them from noise. does the sheath earth to the sensor body?

i would advise running the heater ground direct to battery or body, and keeping away from the ECU earth (or is there differet "earth" and "signal earth" ont he ECU?. kinda defeats the purpose of having signal wires grounded there, and then pumping 1 or 4 amps there with a heater..
I would advise using power from fuel pump to flick a relay... cos then the ECU can be energised for a long time and not burn out the heater.. it will onyl be on when the fuel pump is on.. ie, running.
i ran heater power to a good chassis ground, and the signal earth to the (megasuirts) ground..
i also had sheilded wire, grounded at one end (for all sensors)