Although life histories are shaped by temperature and predation, their joint influence on the interdependence of life-history traits is poorly understood. Shifts in one life-history trait often necessitate shifts in another-structured in some cases by trade-offs-leading to differing life-history strategies among environments. The offspring size-number trade-off connects three traits whereby a constant reproductive allocation (R) constrains how the number (O) and size (S) of offspring change. Increasing temperature and size-independent predation decrease size at and time to reproduction which can lower R through reduced time for resource accrual or size-constrained fecundity. We investigated how O, S, and R in a clonal population of Daphnia magna change across their first three clutches with temperature and size-independent predation risk. Early in ontogeny, increased temperature moved O and S along a trade-off curve (constant R) toward fewer larger offspring. Later in ontogeny, increased temperature reduced R in the no-predator treatment through disproportionate decreases in O relative to S. In the predation treatment, R likewise decreased at warmer temperatures but to a lesser degree and more readily traded off S for O whereby the third clutch showed a constant allocation strategy of O versus S with decreasing R. Ontogenetic shifts in S and O rotated in a counterclockwise fashion as temperature increased and more drastically under risk of predation. These results show that predation risk can alter the temperature dependence of traits and their interactions through trade-offs. © 2018 The Authors. Ecology and Evolution published by John Wiley & Sons Ltd.