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 temperature trends [11-12], and show that a substantial fraction (1.0°C [0.4°-1.6°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 (+63% [20%-106%] since 1950) and persistence (+45% [12%-77%]) are not captured by any of the 32 climate model flow simulations analyzed. The few simulations reaching the observed warming trends in extreme heat have weak dynamical changes, with a decrease in occurrence of southerly flows, indicating that they capture the warming trend for the wrong reasons. 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 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 recent 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.