The concern about global climate change has heightened the need to understand past climatic variation. Temperature variation during the past thousands of years can be estimated from the relative abundances of fossils of various organisms in lake sediments. The past temperatures thus reconstructed suggest several periods of cooling and warming, and it is important to understand how much of the seeming variation is really statistically significant. The paper proposes an inference approach based on the SiZer method. Several different smooths of the reconstructed temperature are considered simultaneously making possible inferences about significant temperature trends at different time scales. The proposed method is applied to temperature reconstruction using a diatom fossil-based data set collected in the Finnish Lapland. The paper also suggests modifications and extensions to the original SiZer method that the present application calls for.