The yellow weather warning is in place from 4pm to 8pm on Tuesday.
York, Leeds, Wakefield and Selby are covered by the yellow weather warning for thunderstorms, while also remaining under the red warning for extreme heat.
Elsewhere, Bradford, Ripon, Leyburn, Thirsk, Malton, Skipton, and Middlesbrough and their surrounding areas can also expect thunderstorms, according to the Met Office. These areas are also under an amber warning for extreme heat.
The Met Office warned that the thunderstorms could damage buildings and structures - and power supplies may be interrupted by lightning strikes.
"Sudden strong and gusty winds may cause damage to temporary structures with a small chance of flying debris," the forecaster added.
The warning comes after a day of extreme heat, as wildfires blazed around the country and the UK experienced temperatures above 40C for the first time. The record was broken at London Heathrow at 12,50, where the mercury had soared to 40.2C.
At least 29 observation sites across England have provisionally broken 2019’s previous UK record temperature of 38.7C, from Bramham, in West Yorkshire, to Charlwood, in Surrey, the Met Office said.