Freight services were suspended for several hours to give priority to passenger trains.
Tracks can buckle once rail temperatures pass a certain threshold, a result of the steel expanding in the heat, said Piotr Hamarnik, a spokesperson for the operator, PKP PLK.
"Train speeds are reduced first; in more serious cases, services are suspended," he said.
Faults were reported on several lines in southern Poland, where replacement bus services were arranged and some trains diverted.
Speed restrictions remain in place on other affected routes, and a regional operator in Silesia said a dozen trains had been cancelled on one of its key routes.
The national carrier, PKP Intercity, is allowing passengers to use its tickets on other train operators, and has waived the usual fee for refunds until 2 July.
Extra staff are on hand at major stations across the country, including in Warsaw, Gdańsk, Kraków and Wrocław, to help affected travellers.
Forecasters expect temperatures of up to 36°C (96.8°F) in southern Poland on Tuesday, rising to 37°C (98.6°F) on Wednesday.
Record temperature at Śnieżka
Meanwhile, a temperature of 25.7°C (78.3°F) was recorded at the Śnieżka weather station, at 1,603 metres in the Karkonosze mountains, according to staff at the local national park.
It is the highest reading since measurements began at the site, run by the IMGW institute, and half a degree above the previous record of 25.2°C (77.4°F), set in August 1982.
The reading was taken on Sunday but only confirmed on Monday.
"The temperature was recorded yesterday, although it did not appear among the readings presented hourly."
"Today, following verification by meteorologists, it was confirmed as a record," park staff said.
Śnieżka is the highest peak in the Sudetes, located in the Karkonosze Mountains.
(ał)
Source: PAP