The application platform, varmecheck.dk, states that applications can be sent from 10am on Tuesday and for the next eight weeks.
The tax-free cash payout or varmecheck of 6,000 kroner was approved by parliament last spring in response to rising energy prices and sent out automatically in August to households which met set criteria.
Some 411,000 households in Denmark received the money, which was intended to help people struggling with additional costs caused by the energy crisis.
The application platform can be used by households which are eligible for the money but did not receive it during the original payment round.
Households with a collective pre-tax income of under 706,000 kroner were eligible for the one-off cash boosts. Additionally, the household should be primarily heated by individual gas heaters (or have experienced similar increases to bills as such homes) or be located in a district heating area in which the heating is produced by at least 65 percent gas.
Errors in registration data may have resulted in households which met the criteria not receiving payments automatically in the original round, the Danish Energy Agency said at the time.
READ ALSO: How to apply for Denmark’s 6,000 kroner energy relief if you were missed by automatic payments
The varmecheck scheme has been extensively discussed in parliament. The previous, single-party Social Democratic government received criticism from opponents after some people were sent the money even though they did not fulfil the criteria, for example because they had replaced their gas boilers but the registration data on their homes was outdated.
Earlier this year, it was confirmed that up to 10,600 homes received the original payment in error. The Danish Energy Agency said between 1.6 percent and 2.6 percent of recipients were not actually eligible for the relief.