Importance: Hypothermia initiated at less than 6 hours after birth reduces death or disability for infants with hypoxic-ischemic encephalopathy at 36 weeks' or later gestation. To our knowledge, hypothermia trials have not been performed in infants presenting after 6 hours. Objective: To estimate the probability that hypothermia initiated at 6 to 24 hours after birth reduces the risk of death or disability at 18 months among infants with hypoxic-ischemic encephalopathy. Design, Setting, and Participants: A randomized clinical trial was conducted between April 2008 and June 2016 among infants at 36 weeks' or later gestation with moderate or severe hypoxic-ischemic encephalopathy enrolled at 6 to 24 hours after birth. Twenty-one US Neonatal Research Network centers participated. Bayesian analyses were prespecified given the anticipated limited sample size. Interventions: Targeted esophageal temperature was used in 168 infants. Eighty-three hypothermic infants were maintained at 33.5°C (acceptable range, 33°C-34°C) for 96 hours and then rewarmed. Eighty-five noncooled infants were maintained at 37.0°C (acceptable range, 36.5°C-37.3°C). Main Outcomes and Measures: The composite of death or disability (moderate or severe) at 18 to 22 months adjusted for level of encephalopathy and age at randomization. Results: Hypothermic and noncooled infants were term (mean [SD], 39  and 39  weeks' gestation, respectively), and 47 of 83 (57%) and 55 of 85 (65%) were male, respectively. Both groups were acidemic at birth, predominantly transferred to the treating center with moderate encephalopathy, and were randomized at a mean (SD) of 16 (5) and 15 (5) hours for hypothermic and noncooled groups, respectively. The primary outcome occurred in 19 of 78 hypothermic infants (24.4%) and 22 of 79 noncooled infants (27.9%) (absolute difference, 3.5%; 95% CI, -1% to 17%). Bayesian analysis using a neutral prior indicated a 76% posterior probability of reduced death or disability with hypothermia relative to the noncooled group (adjusted posterior risk ratio, 0.86; 95% credible interval, 0.58-1.29). The probability that death or disability in cooled infants was at least 1%, 2%, or 3% less than noncooled infants was 71%, 64%, and 56%, respectively. Conclusions and Relevance: Among term infants with hypoxic-ischemic encephalopathy, hypothermia initiated at 6 to 24 hours after birth compared with noncooling resulted in a 76% probability of any reduction in death or disability, and a 64% probability of at least 2% less death or disability at 18 to 22 months. Hypothermia initiated at 6 to 24 hours after birth may have benefit but there is uncertainty in its effectiveness. Trial Registration: clinicaltrials.gov Identifier: NCT00614744.