We are in Spain and it's 38 degrees today...thought I'd add my 2p and pass on some tips we've been given that seem to work!
loose flowy clothes are coolest, so a loose cotton dress is better than a strappy top
at night put her in a sleeveless vest or tshirt rather than just a nappy, as lingering sweat can cause a chill but a vest or top absorbs it. Might end up a bit damp but it's better than a chill!
at night put a fan pointing at the wall, as direct air can cause a chill too, plus dry nose, cough etc whereas pointing it at the wall diffuses the cool air around the room
paddling pool is a godsend! put in the shade.
wide brimmed hat is great, keeps shoulders and neck shady
tepid baths and cool sponges are good too, especially on the face and neck as someone else already suggested
sleeping in the hottest part of the day is good as little ones can get exhausted in this kind of heat
room temp water is more hydrating than cold water because your body pushes cold water through a lot more quickly so there might be lots more wet nappies but the benefit of the water is not being taken
whizz a melon in the blender and freeze it for healthy lollies, or whizz watermelon and honeydew and make stripy ones
Hope this helps, and hope the heatwave passes soon!