Over the last 70 years, extreme heat has been increasing at global scale [1,2], with a rapid rate in several regions including Western Europe [3]. Climate models broadly capture heat trends globally [1], but exhibit systematically weaker extreme heat trends than observations in Western Europe [4-6], together with a weaker summer warming [7,8]. The causes of this mismatch, confirmed here by the analysis of 273 latest generation coupled climate simulations, among which only a handful of them overpass observed trends, are not well understood. Here we use a circulation analogue approach [9,10] to identify the dynamical contribution to daily maximum temperature trends [11-12], and show that a substantial fraction (0.8°C [0.2°-1.4°C] of 3.4°C per global warming degree) of the trend is due to circulation changes, largely due to increases in southerly flows over Western Europe. Their rapid increase in frequency (+43% per global warming degree [10%-76%] since 1950) and persistence are largely underestimated in the 32 climate model flow simulations analyzed, as well as their overall dynamical contributions to temperature trends. The few simulations reaching the observed warming trends in extreme heat have weaker and non-significant dynamical changes, indicating compensating biases in dynamical and thermodynamical trends. These model biases in circulation trends can be due to a systematically underestimated or erroneous representation of the circulation response to external forcing, or to a systematic underestimation of interdecadal variability, or both. The former implies that future projections are too conservative, the latter that we are left with deep uncertainty regarding the pace of future summer heat in Europe: the current strong trend could weaken or increase in future decades. This calls for caution when interpreting climate projections of heat extremes over Western Europe, in particular in view of adaptation to heat waves.