Distance required between two wires to avoid EMI
So you have a 2,000 watt load to a resistive-heater and a motor that has a spark-generating slip-ring. Lets model this as 10 amps and 200 volts, our trash generator.

We'll just consider the HFI, the magnetic field coupling. (The other answer provides electric field coupling.)

For worse case, assume 4 meters of wire in the temperature sensor, with 4 millimeter of spacing between the SenseWire and the ReturnWire.

We'll model this magnetic coupling as a SINGLE transmitter wire (we place the RETURN wire at infinity and get no flux cancellation, thus a worst-case trash generator), and a loop 4meters by 4 milliMeters which is the Receiver). Math?

Vinduce = [MU0*MUr * LoopArea / (2*pi*Distance)] * dI/dT

dI/dT (with NO motor sparks) is 10amps * 377 = 3,770 amps/second

Now let MU0 be 4*pi*1e-7 Henry /meter, let MUr be 1 (air, copper)
and the Vinduce becomes

Vinduce = [2e-7 * Area/Distance] * di/dT

and substituting

Vinduce = 2e-7 *(4meter * 4mm)/4mm * 3,770

Note we assumed the distance between Transmitter and Receiver, inside your "3 wires twisted together", is also 4mm.

Vinduce = 2e-7 * 4 * ~~ 4,000 = 2*4*4 * 1e-7 * 1e+3

Vinduce = 32 e-4 = 3.2 milliVolts

Note motor sparks will be 100X or 1,000X faster, raising the trash coupling 100X or 1,000X.