Vertical profiles of isotope (delta O-18 or delta D) values versus altitude (z) from sea level to high altitude provide a link to cyclones, which impact most ice core sites. Cyclonic structure variations cause anomalous variations in ice core delta time series which may obscure the basic temperature signal. Only one site (Mount Logan, Yukon) provides a complete delta versus z profile generated solely from data. At other sites, such a profile has to be constructed by supplementing field data. This requires using the so-called isotopic or d thermometer which relates delta to a reference temperature (T). The construction of gapped sections of delta versus z curves requires assuming a typical atmospheric lapse rate (d delta/dz), where T is air temperature, and using the slope (d delta/dT) of a site-derived d thermometer to calculate d delta/dz. Using a three-layer model of a cyclone, examples are given to show geometrically how changes in the thickness of the middle, mixed layer leads to the appearance of anomalous delta values in time series (producing decalibration of the delta thermometer there). The results indicate that restrictions apply to the use of the delta thermometer in ice core paleothermometry, according to site altitude, regional meteorology, and climate state.