Our government may find itself in legal hot water when it begins shutting off same in federal restrooms around the nation.

The hot water cutoff, reported here Monday, is supposed to save oodles of oil. Idea is to show the nation and OPEC oil producers that Uncle Sam is no cream puff and can make sacrifices -- via his bureaucrats -- when the going gets tough. The hot-water ban applies to most restrooms and most kinds of sinks, wherever they may be.

The hotwater cutoff will continue to be total. Hot water will continue to be available in health rooms and cafeterias. One suspects that VIPs will get exemptions for their private bathrooms, no doubt for sound reasons of national security. Would you have the president extend a dirty hand to the premier of China? Not likely.

Federal officals are totally serious about the validity of the hot water cutoff. They have ben stunned -- and angered -- by the somewhat irreverant treatment the bold hot water cutoff received this week in the media. There may be more troubled waters to come. Example:

A lot of callers have wondered who dreamed this one up, and who does he think he is kidding?

Joggers and people who bike to work are wondering whether they will be able to clean up at the office and, if not, will the government issue emergency supplies of deoderandts, or at least let people in croweded offices open the windows?

Some bikers, who travel pollution-free, say they will begin driving again, going counter to President Carter's campaign for people to walk, bike, carpool or take buses to work.

A high percentage of the bikers and joggers in federal agencies are lawyers.

And many have gone to the books, looking to see whether chief engineer Jimmy Carter or anybody else can cut off hot water.

Several callers said federal rules under the Occupational Health and Safety Act forbid Uncle Sam, or any other employer, from depriving workers of hot water. It is unsafe and unsanitary, they say, and the plan to sue their agencies if necessary.

For lovers of government rationale, here is the complete fact sheet Uncle Sam worked up to justify the hotwater cutoff. The fact that you may not understand it at all could be a point in your favor. The fact sheet:

"shutting off all domestic hot water used in restrooms and slopsinks in government-owned buildings will reduce energy consumption by 47,-625,055,050 BTUs or $4908233 annually. The calculations for the savings are as follows:

"1378597 -- Total people in government owned buildings.

"Times 3 -- Gallons per person per day equals 4128737 total gallons/ person for all government-owned buildings, times 1 -- specific heat of water equals 4128737 times 8.33 lbs, of water per gallon equals 3,438,099 lbs. of water used by all government-owned buildings times 50 -- temperature-105 degrees, total 171,904,960 BTUs per day for all people in government-owned buildings times 252 (equals working days per year) for total of 43,320,050,046 BTUs annually for all government-owned buildings.

"Take the 43,320,050,046 BTUs annually for all government-owned buidings and multiply it by a 10 percent factor for overtime and summer help, and get an additional 4-332,005,046 for a total of 47,625,051,050 for the Total BTUs for all government-owned buildings divided by 1,390,000 BTUs per 1,000 lbs. of steam and that equals 34,282 (m) pounds of steam or $490,233, the dollars saved each month, divided by 42 gallons of heating oil per barrel which equals 10,683 barrels saved annually."

The footnote, if you got this far, says: "The 47,652,055,050 BTU's saved by elimimating hot water usage in the above facilities will save approximately 13,683 barrels of Number 6 fuel oil annually at boiler efficency of 72 degrees."

The above government equation, which justifies the hot water cutoff, applies only to federally owned buildings in the national capital region of Washington, Maryland, and Virginia.