The influence of cooling rate on the intensity of thermoremanent magnetization (TRM) of archaeological baked clays has long been recognized. Throughout the Thellier-Thellier palaeointensity protocols, the difference between the durations of the laboratory and initial archaeological cooling can bias archaeointensities up to 20%. The most commonly used correction consists in an additional laboratory heating step with a cooling rate assumed to be close to the archaeological one. However, estimating the appropriate duration is very tricky because the archaeological cooling depended on several factors, generally unknown, such as the kiln size and organization and the firecraft techniques. This uncertainty questions the impact of a wrong estimation of the archaeological cooling. In other words, could the cure be worse than the disease for accurate archaeointensity determinations? To investigate this issue, we analyzed 35 bricks baked in two modern kilns in known experimental conditions. The smallest and the biggest kilns cooled in 12 and 40 hours respectively. The main magnetic carriers were Ti-poor titanomagnetites and Ti-poor titanohematites, whose relative proportions varied between bricks. After TRM anisotropy correction, average archaeointensities, determined using the Thellier-Thellier protocol, overestimated the expected field intensity by 5%, highlighting the necessity of the cooling rate correction. In order to have a detailed evaluation of the cooling rate effect, we used several slow cooling rates: 0.8, 0.4, 0.2 and 0.1°C/min. The correction factors obtained with the 0.8°C/min cooling ranged between -2% and 21% and were proportional to the TRM fraction carried by Ti-poor titanohematites. Titanohematites contributed three times more to the cooling rate effect than to the NRM intensity. It is not clear if the stronger dependency to cooling rate effect of titanohematites compared to titanomagnetites is intrinsic or due to their grain size. The average intensities corrected by the four different cooling rates are all close to the expected value, which suggests that a precise knowledge of the archaeological cooling duration in a kiln is not essential.