Most mathematical models that assess the vectorial capacity of disease-transmitting insects typically focus on the influence of climatic factors to predict variations across different times and locations, or examine the impact of vector control interventions to forecast their potential effectiveness. We combine features of existing models to develop a novel model for vectorial capacity that considers both climate and vector control. This model considers how vector control tools affect vectors at each stage of their feeding cycle and incorporates host availability and preference. Applying this model to arboviruses of veterinary importance in Europe, we show that African horse sickness virus (AHSV) has a higher peak predicted vectorial capacity than bluetongue virus (BTV), Schmallenberg virus (SBV) and epizootic haemorrhagic disease virus (EHDV). However, AHSV has a shorter average infectious period, due to high mortality, therefore AHSV's overall basic reproduction number is similar to BTV. A comparable relationship exists between SBV and EHDV, with both viruses showing similar basic reproduction numbers. Focusing on AHSV transmission in the UK, insecticide-treated stable netting is shown to significantly reduce vectorial capacity of Culicoides even at low coverage levels. However, untreated stable netting is likely to have limited impact. Overall, this model can be used to consider both climate and vector control interventions either currently utilised or for potential use in an outbreakand could help guide policy makers seeking to mitigate the impact of climate change on disease control.