Rationale Sardinian alcohol-preferring (sP) rats displayed high sensitivity to time schedule and consumed intoxicating amounts of alcohol during the last portion of the dark phase of the light/dark cycle when exposed to daily drinking sessions of one hour, with concurrent availability of multiple alcohol concentrations, and unpredictability of time of alcohol access. Objectives The present study investigated whether sensitivity of sP rats to time schedule extended to operant procedures of alcohol self-administration. Methods In Experiment 1, three different alcohol solutions (10%, 20%, and 30%, v/v) were concurrently available under a Fixed Ratio 4 schedule of reinforcement and with unpredictable time schedule; water was available uncontingently. Experiments 2 and 3 assessed the sensitivity of the motivational properties of alcohol to time schedule; rats were exposed to (a) self-administration sessions under the Progressive Ratio (PR) schedule of reinforcement and (b) sessions of alcohol seeking under the extinction responding (ER) schedule. Results In Experiment 1, number of lever-responses and amount of self-administered alcohol were positively correlated with time of alcohol access during the dark phase. When the self-administration session occurred at the first and latest hours of the dark phase, the amount of self-administered alcohol averaged 0.95–1.0 and 1.55–1.65 g/kg, respectively. In Experiments 2 and 3, values of breakpoint and ER for alcohol were approximately 50% higher when the sessions occurred at the last than first hour of the dark phase. Conclusions The reinforcing and motivational properties of alcohol were sensitive to time schedule and stronger at the end of the dark phase.