BACKGROUND: Climate change is increasing the frequency and intensity of heatwaves. Prior studies associate high temperature with preterm birth. OBJECTIVES: We tested the hypotheses that acute exposure to extreme heat was associated with higher risk of live spontaneous preterm birth (≥20 and <37 completed weeks), and that risks were higher among people of colour and neighbourhoods with heat-trapping landcover or concentrated racialised economic disadvantage. METHODS: We conducted a retrospective cohort study of people giving birth between 2007 and 2011 in Harris County, Texas (Houston metropolitan area) (n = 198,013). Exposures were daily ambient apparent temperature (AT(max) in 5°C increments) and dry-bulb temperatures (T(max) and T(min) >historical [1971-2000] summertime 99(th) percentile) up to a week prior for each day of pregnancy. Survival analysis controlled for individual-level risk factors, secular and seasonal trends. We considered race/ethnicity, heat-trapping neighbourhood landcover and Index of Concentration at the Extremes as effect modifiers. RESULTS: The frequency of preterm birth was 10.3%. A quarter (26.8%) of people were exposed to AT(max) ≥40°C, and 22.8% were exposed to T(max) and T(min) >99(th) percentile while at risk. The preterm birth rate among the exposed was 8.9%. In multivariable models, the risk of preterm birth was 15% higher following extremely hot days (hazard ratio [HR] 1.15 (95% confidence interval [CI] 1.01, 1.30) for AT(max) ≥40°C vs. <20°C; HR 1.15 (95% CI 1.02, 1.28) for T(max) and T(min) >99(th) percentile). Censoring at earlier gestational ages suggested stronger associations earlier in pregnancy. The risk difference associated with extreme heat was higher in neighbourhoods of concentrated racialised economic disadvantage. CONCLUSIONS: Ambient heat was associated with spontaneous preterm birth, with stronger associations earlier in pregnancy and in racially and economically disadvantaged neighbourhoods, suggesting climate change may worsen existing social inequities in preterm birth rates.