The amber warning is in place for the whole of Sunday (July 17), when temperatures are being forecast to reach 28C.
According to the Met Office: "Some exceptionally high temperatures are possible during Sunday and could lead to widespread impacts on people and infrastructure.
"Population-wide adverse health effects are likely to be experienced - not limited to those most vulnerable to extreme heat - leading to potential serious illness or danger to life.
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"Government advice is that 999 services should be used in emergencies only - seek advice from 111 if you need non-emergency health advice.
"Substantial changes in working practices and daily routines likely to be required.
"Significantly more people are likely to visit coastal areas, lakes and rivers leading to increased risk of water safety incidents.
"Delays on roads and road closures are possible, along with delays and cancellations to rail and air travel, with potential for significant welfare issues for those who experience even moderate delays."
It said it is likely that the warning could be extended into the following day (Monday, July 18).
"Temperatures will build again later this week and over the coming weekend, likely peaking on Sunday and Monday," it says.
"Some exceptionally high temperatures are possible and cumulative effects of warm nights and hot days are expected to bring widespread impacts to people and infrastructure.
"This period of hot weather is expected to continue into the early part of next week, hence an update extending this warning into Monday is likely."