Ingredients necessary for the formation of thunderstorms are
... moisture, rising unstable air (air that keeps rising when given a nudge), and a lifting mechanism to provide the “nudge.” (source)
as well as
... MOISTURE, INSTABILITY, and LIFTING. Additionally, there is a fourth ingredient (WIND SHEAR) ... (source)
and they depend on the local, regional or overregional weather situation, can have seasonal aspects, may be be bound to one or more circulation patterns or just depend on the weather ;-)
Thunderstorms can form isolated, e.g. in the afternoon when during the day the conditions have built up and labilization took place from different ground types, orography, sunshine duration/intensity/angle or "drops" of cold air high up in the troposphere. These are Orograhic thunderstorms or air mass thunderstorms. They are usually (but not always) short lived (hours), local and occur in the afternoon and last until the early night.
Or thunderstorms can form along a frontal line that separates cold from warm air mass and that moves into the warm, moist air, causing it to rise to great height where it starts to condensate. This phenomenon is called a cold front or in a special form a squall line (radar image) and labilization is here the result of the difference in air temperature and moisture on a relatively narrow frontal line. Frontal system have considerable length (100s or rarely thousands of km) and moves swiftly over long distances. These frontal systems can be part of the cylones in the temperate zones (not the tropical cyclones, those are different and I leave them out here, though they house embedded thunderstorms as well) and move with the prevailing western drift there. Such a frontal passage usually doesn't last long, comes with a significant drop in air temperature when passing overhead and a significant weather change and veering wind, on the northern hemisphere.
All these forms are expressions of convective weather, vertical movement of air caused by labilization.
Otoh, heat waves are frequently simply the result of dry and hot air being transported by advection, which is not bound to a local scale alone. For example the Sahara air to central Europe. This air is hot and very dry, and it simply lasts until the weather situation changes and different airmasses come along, e.g. of Atlantic origin. There won't be thunderstorms, then, because there's not enough moisture. Such a weather situation frequently happens on the Canaries (just as an example), it leads to a hot and extremely dry atmosphere until great height, with a cool layer underneath, for example 23°C at sea level, ~30° at 500m ASL with an inversion in between, and 35°C around the summits between 2,000 and 2,500m ASL. This is absolutely stable and not even slightly conducive for the formation of convection or any kind of precipitation (except sand :-/).
tl.dr: No, it is not normal, but it can happen. There is no general rule and it is not the absolute temperature that causes thunderstorms, but differences in temperature and moisture that cause labilization and thus convection.
