Greater Rheas (Rhea americana) are precocial birds that show uniparental male care. We evaluated the extent of nest attention by males and estimated its effect on viability and survival of eggs. We assessed whether male absences during incubation were constrained to avoid embryos reaching lethal temperatures or to minimize risk of egg predation. We estimated (1) effect of nest attention on viability of eggs by comparing egg temperature in nests with and without male attention; and (2) effect of male care on egg predation, by comparing survival of eggs in nests with and without male care. Rhea males attended the eggs for 42 days, but effective incubation started 5–7 days after laying of the first egg. The proportion of time that males spent at the nest increased from 64% during egg laying (days 1–10) up to 97.5% during mid and late incubation (days 20–40). Male absences occurred at the warmest hours of the day and their lengths were positively correlated with the temperature of the environment. Male nest attention reduced the rate of egg losses and kept eggs above lower lethal temperatures for embryos during the night. We also estimated relative cost of parental care after hatching by comparing the time allocated to feeding and vigilance by males with chicks, males in nonreproductive groups, and nonreproductive solitary males. Males took care of the chicks for 4–6 months. They allocated less time to feeding and more time to vigilance than males in groups of adults or solitary males. Investment in vigilance decreased as chicks aged. Our results indicate that Greater Rhea males would require high levels of energetic reserves to start a breeding attempt. That high demand could explain why less than only 20% of the males attempt to nest during a breeding season.