## 1 Introduction  
Heat waves (HW) are extreme weather high-temperature events that may pose a risk to ecosystems and socio-economic activities, in general, and particularly to human health [1]. These phenomena are frequently disregarded since they do not cause as dramatic visual impacts as many other extreme weather events such as storms and tornados. However, HW may negatively affect, for example, agriculture, forest fires, power supply for cooling, animal and human morbidity, and mortality, particularly of vulnerable people. HW are a synoptic scale weather phenomena that impact large regions, countries, and even great parts of a continent. Their effects may be locally amplified by various factors such as the type of land coverage, altitude, slope orientation of orography, and proximity to water bodies. In medium to large cities, HW may be strongly amplified by the nature of predominant materials in what is known as the urban heat island effect [2]. Many HW studies have been published with a vast range of objectives, such as for example to evaluate the HW spatial extent [3,4] and identify the responsible large-scale physical mechanisms such as blocking [5, 6, 7]. Other studies focused on the health impacts of HW [8, 9, 10] or their consequences to forest fires [11] and agriculture [12]. Other authors have studied changes in HW characteristics trends in the past [13] and in future climate change projections [14,15]. These types of studies may have different objectives, but most of them are concerned with the changing health impacts in future climate scenarios [16]. This is particularly relevant for cities due to the amplification of HW effects by the urban heat island effect, but it is also related to the fact that cities are densely populated areas, frequently with a large proportion of vulnerable people, and where health emergency services may face peak affluence during such events. [PERSON] et al. [7] studied the recent trends of HW characteristics in European cities. They devised a HW hazard index and found that most of the capitals revealed significant positive trends of HW hazard characteristics especially in central-eastern and southeastern Europe. They also concluded that minor index increases were observed in most of the northern capitals and decreases in several northern and especially southwestern cities. [PERSON] et al. [17] applied different HW definitions to study long-term (1893-2017) trends of HW duration and frequency for Berlin. They found a general positive trend amongst HW definitions but with the respective magnitude depending on the definition and trend estimation method. [PERSON] et al. [18] also report recent positive trends of HW duration, intensity, and frequency in Extremadura (Spain). However, [PERSON] et al. [7] did not find significant trends in some HW indices for Lisbon in the recent past, unlike for other European cities. [PERSON] et al. [19] studied HW for the recent climate (1976-2015) over southwestern Europe and identified increases in the HW frequency over the Iberian Peninsula (IP). They report an association between HW and synoptic conditions related to anticyclonic blocking over the region. Most HW studies usually consider the number of HW and HW days, HW duration, and intensity. These measures are relevant to evaluate HWs but of limited value for practical purposes. Apart from these, this study also considers other HW measures that are more relevant for the impact and adaptation studies such as the month of their occurrence, the 'accumulated' warming during a HW associated heat stress, and the relief that people may have during the nights of HW days. As such, the methodology suggested here is of more practical value when devising adaptation measures for future climate scenarios. This analysis is performed firstly for present climate conditions but extends for medium- and long-term future climate projections. Changes relative to the present climate are of primary importance to evaluate their impacts and to develop adaptation and mitigation measures.