In the UK and in reference to turf, rapid evaporation of the water is the only reason not to water in bright sunlight; it is indeed a myth that water droplets can burn leaves (there's an interesting tale as to how this myth came about) and nor will the water get too hot and burn the turf or roots. Hopefully you are using a hose and sprinkler to water with, first, and second, the best time to water is after 4pm or later, preferably after 5 or 6 pm, and when the sun is not on the area. In particular, ensure the sprinkler is covering the edges of the turf, round the outside, including any bare soil it might be edged up with - those areas are the most likely to dry out. Set the sprinkler to run for at least half an hour (but preferably an hour) on each area before moving it to cover another area. It is better to water for longer when you do water rather than giving less daily. Even so, whilst it is so hot and especially if the sun is out, you may need to water daily or every other day till the weather calms down again, as it's new turf. You can check by feeling the edges of the turf, especially if it butts up to soil rather than a hard surface - that's where it dries out first.
Lastly, if you really have to because you're not going to be around to do it in the evening, water any time - sports fields and golf courses commonly run sprinklers during bright sunlight without harm, but it is a better use of the water to do it early evening, when it will have the best chance to penetrate through the turf, down to the roots and the soil beneath, and not evaporate so readily overnight. If you do have to water when its hot and sunny in the middle of the day, you will need to run the sprinkler for longer.
When this heatwave is over, water in the same way (evenings or early morning) but less often - maybe every 4 or 5 days, depending on air temperatures/sunshine, especially if there is light rain about. You will not need to water if there's heavy or very persistent rain. By the end of August, we will start having increasingly heavy dews overnight, which will help with moisture supply, and by then, your turf should hopefully be well on the way to rooting into the soil beneath.