Since the release of the Fifth Assessment Report by the IPCC in 2013, evidence is mounting that the impacts of global warming on society and ecology actually depend stronger on seasonal extremes (e.g., summer peak temperature) than on trends in annual mean. This is true especially for tropical regions, where extremes have become the greatest threat to ecosystems. However, little is known about the rates of change in mean and extremes, currently or in future. Lack of high-resolution data from past warm climates (which serve as analogues) and lack of advanced data-analytical methods explain this knowledge deficit. To overcome it, we propose here to (1) utilize a database from high-resolution coral proxy records and (2) apply advanced simulation techniques from statistical science. We seek quantitative answers to the following questions. (A) What is the rate of change in sea surface temperature (SST)? (B) What is the amplitude of the seasonal SST cycle? (C) What is the rate of change in occurrence of seasonal SST extremes? This leads to a better assessment of the ultimate question (D) about the relation between long-term climate warming and the occurrence of seasonal extremes. SEARCH builds a database from existing and new (bi-)monthly resolved records during the (a) Anthropocene, (b) Medieval Climate Anomaly-Medieval Warm Period, (c) Holocene Thermal Maximum, (d) Last Interglacial and (e) Mid-Pliocene Warm Period. SEARCH is supported by new data and modeling expertise from eight cooperation partners within SPP 2299. SEARCH will impact academic climate research, climate modeling, applied climate risk assessments – and the future scientific careers of five students.