Biodiversity can provide insurance against environmental change, but only if species differ in their response to environmental conditions (response diversity). Wild bees provide pollination services to wild and crop plants, and response diversity might insure this function against changing climate. To experimentally test the hypothesis that bee species differ in their response to increasing winter temperature, we stored cocoons of nine bee species at different temperatures during the winter (1.5–9.5 °C). Bee species differed significantly in their responses (weight loss, weight at emergence and emergence date). The developmental stage during the winter explained some of these differences. Bee species overwintering as adults generally showed decreased weight and earlier emergence with increasing temperature, whereas bee species overwintering in pre-imaginal stages showed weaker or even opposite responses. This means that winter warming will likely affect some bee species negatively by increasing energy expenditure, while others are less sensitive presumably due to different physiology. Likewise, species phenologies will respond differently to winter warming, potentially affecting plant–pollinator interactions. Responses are not independent of current flight periods: bees active in spring will likely show the strongest phenological advances. Taken together, wild bee diversity provides response diversity to climate change, which may be the basis for an insurance effect.