The temperatures seen next week edge close to the hottest temperatures Hawke's Bay has on record.
NIWA forecaster Maria Augutis said Napier's hottest temperature on record since 1931 was 37.5C on December 29, 1994.
It's had several days above 35C in its history, with 35.6C on January 27, 1952 recorded as Napier's fifth highest temperature.
Hastings' hottest recorded temperature since records from 1971 began was 37.1C on February 2, 2009.
The fifth highest temperature in Hastings on record is 35.2C on January 12, 1979.
MetService meteorologist Tom Adams said there was "the potential for a heatwave" in Hawke's Bay.
A period of warm weather is considered a heatwave when the maximum temperature is 5 degrees hotter than the monthly average for five consecutive days.
Adams said the period of hot weather was due to Foehn wind.
A northwesterly wind brings moist air from the tropics which condenses as it blows into the east coast of New Zealand and releases hot air.
The hot temperatures bring with it a high UV index rating of 12 which is considered extreme.
Sun protection must be worn from early morning until 5.30pm even on cloudy days.
Information from NIWA said a UV Index rating of 12 corresponds to a burn time of around 12 minutes.
There is no upper limit of the UV index rating but in New Zealand it tends to peak at 13-14 in the far North.
Temperatures will also remain hot throughout the night in the high teens and low 20s, temperatures Adams describes it as "quite unpleasant" for sleeping.
The heat could also cause scattered thunderstorms. Hawke's Bay was facing a moderate risk of severe thunderstorms starting Wednesday afternoon and going through the evening.
Thunderstorms were expected to develop between 4pm and 9pm over inland parts of Hawke's Bay and Gisborne.
Adams said between 20mm and 40mm of rain per hour could be expected.
Rainfall of this level can cause surface or flash flooding and hazardous driving conditions.
It is expected to move offshore later in the night.
At this stage, weather is expected to remain warm with no cold snaps ahead for the next three or four weeks, Adams said.