Thermal tolerance shapes organisms' physiological performance and limits their biogeographic ranges. Tropical terrestrial organisms are thought to live very near their upper thermal tolerance limits, and such small thermal safety factors put them at risk from global warming. However, little is known about the thermal tolerances of tropical marine invertebrates, how they vary across different life stages, and how these limits relate to environmental conditions. We tested the tolerance to acute heat stress of five life stages of the tropical sea urchin Lytechinus variegatus collected in the Bahía Almirante, Bocas del Toro, Panama. We also investigated the impact of chronic heat stress on larval development. Fertilization, cleavage, morula development, and 4‐armed larvae tolerated 2‐h exposures to elevated temperatures between 28–32°C. Average critical temperatures (LT
50) were lower for initiation of cleavage (33.5°C) and development to morula (32.5°C) than they were for fertilization (34.4°C) or for 4‐armed larvae (34.1°C). LT
50 was even higher (34.8°C) for adults exposed to similar acute thermal stress, suggesting that thermal limits measured for adults may not be directly applied to the whole life history. During chronic exposure, larvae had significantly lower survival and reduced growth when reared at temperatures above 30.5°C and did not survive chronic exposures at or above 32.3°C. Environmental monitoring at and near our collection site shows that L. variegatus may already experience temperatures at which larval growth and survival are reduced during the warmest months of the year. A published local climate model further suggests that such damaging warm temperatures will be reached throughout the Bahía Almirante by 2084. Our results highlight that tropical marine invertebrates likely have small thermal safety factors during some stages in their life cycles, and that shallow‐water populations are at particular risk of near future warming.