Over several decades the physician and astronomer Wilhelm Olbers (1758--1840) has consistently made air temperature and pressure readings in Bremen and written many manuscripts to meteorological topics. Few of his works were published, most fell into oblivion, so also Olbers' measurements of temperature and pressure from the years 1803--1822, although these meteorological observations are the first continuous and reliable measurements of this kind in Bremen. In this article we look at the monthly and annually averaged temperatures from 1803 to 1822 (see \Fig{T03_22}), which are taken from the literary legacy of Olbers and are partially reconstructed. We discuss the linkage of these series of measurements to the well-known Bremen temperature series, which begins in 1829 and is today continued by the German Weather Service (DWD). The method we propose for this adjustment is based on the extremely high correlation which the annually averaged data of the Bremen time series have with corresponding data from other monitoring sites. We use data from De Bilt, Berlin, Prague, Stockholm and Hohenpeissenberg. The result is a temperature time series for Bremen from 1803 to today, which has only a short interruption and may be regarded as homogeneous at least to some extent.