Hot water, an illegal substance in U.S. restrooms since last spring, will soon begin to flow freely from federal faucets.

Government officials -- with some friendly nudges from the Reagan administration -- have decided to end the energy-conservation experiment launched in an attempt to cut Uncle Sam's hot water bill.

It did reduce consumption of fuel oil in the Washington area, home to 400,000 federal civilian and military personnel. But it generated too much heat from employes who found it unpleasant, and unhealthy, to wash up all winter in icy water.

Readers were tipped off to the hot-water cutoff here last June 9. Within days, engineers moved through hundreds of federally owned buildings cutting off hot water in bathrooms, or where that was impossible, removing hot water handles from faucets. The hot-water cutoff became a source of delight to television commentators and newspapers editorial cartoonists.

Officials at the General Services Administration pointed out that significant savings could be made. And it was the sort of symbolic PR gesture that the Carter administration loved. U.S. engineers came up with complicated charts and data explaining how much water was wasted from the typical federal spigot.

Federal workers were not impressed. Many saw it as a chicken-dig at the bureaucracy by an administration that had also forced people to give up free parking spaces at the office.

Insiders have advised this column that the hot water will be returning within the next few weeks. Some taps will be hot today. It depends on how long it will take engineers and maintenance personnel to undo what they were ordered to do last year