he Army overspent its heating budget here, leaving 10,000 soldiers and their families shivering in unheated quarters with temperatures dipping to 30.

"We've turned off all the heat . . . except in health, welfare and morale activities," such as hospitals and schools, said Maj. Bill Grove, public affairs officer. "These measures were necessary to provide adequate energy for the critical summer season."

Grove said Fort Polk, headquarters for the 5th Mechanized Infantry Division, received nearly $9.6 million for energy use in the fiscal year that began Oct. 1, 1982.

Officials, however, recently discovered the budget had been overspent and were forced to turn off the heat as a cost-saving effort. Grove said officials were trying to find out why the winter allocation was used so quickly.

He said no heat or air conditioning will be used on the post, except in exempted buildings, until May 15, when the air conditioning season begins.

He said gas, electric and oil heating systems were cut off March 18 in the living quarters of the commanding general and two assistant division commanders.

Heat was shut off in barracks and post houses this week, even though overnight temperatures slipped into the 30s.

Heat went off Tuesday in troop quarters and most of the 2,873 family houses, which have 7,60 residents, Grove said.

He estimated about 250 houses were exempted from the policy for various reasons.