In fact, passengers may face upto a 12-hour delay before completing immigration formalities, and some may be confined to their aircraft if the lobbies get clogged with incoming passengers in one of the busiest airports in the world.
British immigration officials posted in India and other countries have been offered free travel to London to stand in for the officers who will be on strike.
They could also spend some time with their families when they volunteer for this duty, officials said.
Heathrow chief operating officer Norman Boivin said there was a danger of "gridlock".
The strike is scheduled for 30 November, but it will be days before situation returns to normal if the strike leads to the anticipated 'gridlock'.
A spokesman for Prime Minister David Cameron said: "At the very least there will be longer queues and people will have to wait longer at borders," and added that the government was still working on contingency plans and gathering information on the impact of the strikes.
In a letter to all airlines operating into Heathrow, Boivin said: "The delays at immigration are likely to be so long that passengers could not be safely accommodated within the terminals and would need to be held on arriving aircraft".
He added: "This in turn would quickly create gridlock at the airport with no available aircraft parking stands, mass cancellations or departing aircraft and diversions outside the UK for arriving aircraft.
Modelling of the impacts of strike action on passenger flows at Heathrow shows that there are likely to be very long delays of up to 12 hours to arriving passengers.
Public sector workers are going on strike because of proposed changes to pensions for public sector workers, and spending cuts.
The government says that as people live longer, the cost of funding public sector pensions is "unsustainable", and wants most public sector workers to pay more into their pensions, work for longer, and accept a pension based on a "career average" salary, rather than the current final salary arrangement.
Employee unions say the proposals will leave their members paying more and working longer for less.
Boivin has asked aircraft carriers to cut their 'load factors' by half on international flights to relieve the pressure.
The Home Office is pulling in border agency staff who are not union members and civil servants from Whitehall to carry out immigration checks.
In a statement, the department said it was too early to speculate on how many people would join the strike, and that it was exploring all options to minimise disruption.
Rob Whiteman, chief executive of the UK Border Agency, said they had spent the last weeks and months considering all options to ensure there were prepared for union action.