The method produces a hydrocarbonaceous fluid (a liquid mixture of hydrocarbons, or in other words a mixture of hydrocarbons which is liquid at ambient room temperature and atmospheric pressure), which functionally is a liquid hydrocarbon fuel, from a feed of waste plastic. The method can comprise the steps of: (step 1) melting a feed of substantially solid waste plastic in an aerobic atmosphere (for instance, air) whereby a waste-plastic melt is produced; (step 2) distilling at least a portion of the waste-plastic melt whereby a hydrocarbonaceous distillate is produced; and (step 3) collecting the hydrocarbonaceous distillate. That distillate is generally referred to above as a condensate. The method can include the step of comminuting the feed of substantially solid waste plastic into pieces substantially no greater than about 1.5 cm2 prior to step 1. The method can also include the step of adding an effective amount of a cracking catalyst to the waste plastic prior to step 2.