A new solar hot water heating system being installed at the White House costs thousands of dollars more than originally estimated and it probably won't pay for itself in energy savings, officials say.

Intended by President Carter as a showcase for non-polluting energysaving solar technology, the new system is an economic dog, by official White House estimate.

Connstruction work began Monday and is expected to be completed by May 1. The system is designed to supply about 75 percent of the hot water used in the West Wing offices.

When the design was announced to reporters last September, the president's cousin, Hugh Carter, who administers the White House payroll and expenses, said it was supposed to cost $24,000 to install and would cut utility bills by $1,000 a year to start9

However, the lowest bid received on the project was $28,099, more than $4,000 higher than projected. Worse, it was discovered that $7,000 worth of roofing work has to be done before the solar panels can be put in, although White House officials say this work eventually would have been necessary anyway. CAPTION: Picture 1, Workmen begin installing solar heating system on roof of West Wing of the White House. AP; Picture 2, This model shows the design for 32 solar panels being installed on roof for hot water heating. AP