Transmission lines ... have a limited capacity for how much energy they can carry, which is further reduced when they get hot.
The increase in heat, increases the resistance, meaning less power can get through - which isn't ideal when many of us will be using power to keep cool....
....In short, despite the Met Office warning of possible disruption to electricity supplies, the grid is highly resistant. There is spare capacity and distributors are on standby to react to any faults when they do occur.
There may be the odd blackout - but this will more than likely be to localised faults rather than the heat disrupting the grid.
