As more countries make net zero greenhouse gas emissions pledges, it is crucial to understand the effects on global climate after achieving net zero emissions. The climate has been found to continue to evolve even after the abrupt cessation of CO2 emissions, with some models simulating a small warming and others simulating a small cooling. In this study, we analyse if the temperature and precipitation changes post abrupt cessation of CO2 emissions are significant compared to natural climate variations. We find that the temperature changes are outside of natural variability for most models, whilst the precipitation changes are mostly non-significant. We also demonstrate that post-net zero temperature changes have implications for the remaining carbon budget. The possibility of further global warming post-net zero adds to the evidence supporting more rapid emissions reductions in the near-term.