## 1 Introduction  
The Earth is facing a rapid climate warming and population growth [1]. This has implications for lake ecosystem functioning and entails an increased risk of eutrophication, reflecting both increasing external and internal nutrient loading and a shift in top-down control that reduces the zooplankton grazing pressure on phytoplankton [2; 3; 4]. This is especially the case for shallow lakes that are presumed to be the most common and vulnerable lake type to global warming [2; 5; 6]. It should be added that the predicted increase of the world population will demand higher food production and with this trend comes increasing eutrophication [2; 3; 4].  
Several studies have shown positive effects of temperature on both gross primary production (GPP) and ecosystem respiration (ER), often accompanied, however, by reduced net ecosystem production (NEP = GPP \(-\) ER) [7; 8; 9; 10], reflecting that ER theoretically is more sensitive to temperature than GPP. Accordingly we may expect an increasing degree of heterotrophy in shallow lake ecosystems with increasing temperatures [9; 11], as also demonstrated experimentally in a recent cross-European shallow lakes experiment [12]. In contrast, elevated nutrient concentrations (eutrophication) increase metabolic rates, but often the impact is greater on GPP than on ER, leading to an increase in NEP and organic matter accumulation in the sediment [13; 14]. Accordingly, [PERSON] et al. [12] found that higher nutrient availability not only resulted in significantly higher GPP and ER, but also in a significantly lower ER to GPP ratio, indicating that high-nutrient systems are likely to have a lower risk of becoming net heterotrophic than those with lower nutrient concentrations. In addition, a cross-system analysis has revealed that ER and GPP are more coupled in oligotrophic lakes than in eutrophic lakes [12]. However, the interacting effects of temperature and trophic state on productivity/oxygen metabolism are generally not well understood [15; 16]. It is, however, well-established that bacterioplankton production (BACPR) increases with temperature (e.g., [17; 18; 19; 20; 21]), but BACPR is also highly sensitive to changes in lake trophic state and typically increases with increasing eutrophication [17; 18; 22], which is facilitated further at high temperatures [18].  
Global warming not only increases average temperatures, it also enhances the frequency of extreme events such as heat waves [23; 24; 25]. Shallow lakes may be particularly sensitive to heat waves, as their average water temperature will increase more rapidly than in deep lakes [26] and this may lead to a catastrophic shift if metabolism imbalances occur. Thus, some shallow lake studies have shown sudden oxygen depletion and fish kills during extreme climate event including heat waves [27] or when phytoplankton blooms undergo intensive bacterial degradation, often in warm, calm weather [28].  
In the present study, we focused on nutrients, oxygen and oxygen metabolism and BACPR before, during and after a simulated 1-month summer heat wave in shallow lakes. We used data from the longest running mesocosm experimental facility on climate effects on shallow lakes [29], where different temperatures crossed with low and high nutrient levels are employed. We heated the already long-term heated mesocosms an extra 5 \({}^{\circ}\)C during July, to elucidate how lakes in a future warmer world would respond to heat waves. We hypothesized that (1) nutrients would have a strong stimulating effect on GPP, ER, NEP and BACPR, (2) higher temperatures would increase GPP, ER and BACPR but decrease NEP, with the strongest effects at high nutrient concentrations where the nutrient constraints on productivity would be lower and (3) a HW in the warmed mesocosm hosting an already temperature-stressed lake ecosystem might result in sudden dramatic shifts due to imbalances in the metabolism that may lead to sudden changes in oxygen and perhaps have major detrimental impacts on the fish population.