Great Western Railway has extended its essential travel only advice into Friday for passengers travelling into, through or out of amber weather warning areas.
The rail operator says extreme heat can cause rails to expand and buckle, meaning trains may need to run more slowly for safety.
Fewer trains and longer journey times are expected during the hottest parts of the day, with possible short-notice changes or cancellations.
GWR is easing ticket restrictions, allowing tickets from Tuesday to Friday to be used up to and including Tuesday 30 June.
Passengers who do not travel can claim a refund or amend their ticket, while those delayed by 15 minutes or more may be eligible for Delay Repay compensation.
Customers are being urged to check before travelling, allow extra time and carry water.