Step 1: Pain and temperature are carried by the lateral spinothalamic tract. The second-order neurons of this tract cross to the opposite side within the spinal cord, just one or two segments above their entry.
Step 2: Because the fibres have already decussated in the cord, damage to the lateral spinothalamic tract causes loss of pain and temperature on the side opposite to the lesion, below the level of injury. This is why the deficit is contralateral.
Step 3: The distractors carry different modalities. The anterior spinothalamic tract carries crude touch and pressure. Fasciculus gracilis and fasciculus cuneatus form the dorsal column and carry conscious proprioception, fine touch, stereognosis and vibration - none of these produce loss of pain and temperature.
Step 4: Hence the answer is the lateral spinothalamic tract.