The bill was passed on a vote of 293 to 22, with 112 abstentions, Polish state news agency PAP reported.
The draft legislation now heads to the Senate (upper house) floor.
Under the bill, prices on heating from networks will be capped to protect household energy bills.
Moreover, households that use liquefied petroleum gas (LPG) for heating will be eligible for a one-off benefit of PLN 500 (EUR 106), and those that use wood chips will be offered PLN 1,000 (EUR 212), officials said.
Meanwhile, families using heating oil will receive a one-off allowance of PLN 2,000 (EUR 424), and those that use pellets as fuel will be eligible for PLN 3,000 (EUR 636), the PAP news agency reported.
Earlier, the government offered a one-off allowance of PLN 3,000 (EUR 636) for those who use coal for heating.
That bill has since been approved by parliament and signed into law by President Andrzej Duda.
Source: PAP, tvpparlament.pl