The aim of this paper is for the production of oils processed in refineries to come from the pyrolysis of real waste from the high plastic content rejected by the recycling industry of the Basque Country (Spain). Concretely, the rejected waste streams were collected from (1) a light packaging waste sorting plant, (2) the paper recycling industry, and (3) a waste treatment plant of electrical and electronic equipment (WEEE). The influence of pre-treatments (mechanical separation operations) and temperature on the yield and quality of the liquid fraction were evaluated. In order to study the pre-treatment effect, the samples were pyrolyzed at 460 °C for 1 h. As pre-treatments concentrate on the suitable fraction for pyrolysis and reduce the undesirable materials (metals, PVC, PET, inorganics, cellulosic materials), they improve the yield to liquid products and considerably reduce the halogen content. The sample with the highest polyolefin content achieved the highest liquid yield (70.6 wt.% at 460 °C) and the lowest chlorine content (160 ppm) among the investigated samples and, therefore, was the most suitable liquid to use as refinery feedstock. The effect of temperature on the pyrolysis of this sample was studied in the range of 430–490 °C. As the temperature increased the liquid yield increased and solid yield decreased, indicating that the conversion was maximized. At 490 °C, the pyrolysis oil with the highest calorific value (44.3 MJ kg−1) and paraffinic content (65% area), the lowest chlorine content (128 ppm) and more than 50 wt.% of diesel was obtained.