The United Mine Worker Union was released from a temporary back-to-work order yesterday and was left free of government interference to contiue its 102-day strike against the nation's coal industry.

In a blow to the Carter administration's strategy for coping with the strike, U.S. District Judge Aubrey E. Robinson Jr. refused to grant a government request for an extension of the one-week restraining order he issued March 9 under the Taft-Hartley Act.

The order expired at 6 p.m. yesterday, which means the union no longer needs to go through the pretense of obeying it.

Robinson scheduled a hearing March 28 for arguments on a full 80-day Taft-Hartly injuction, but warned the government that evidence sumitted so far to the court is insufficient to warrant granting such an injuction.

"I don't think the government would seriously contend they have enough" evidence for an injuction, said Robinson during a two-hour hearing on the request for the extension. "that is why they came in here for an extension of the TRO," the temporary restraining order, he added.

The effect on the coalfields of Robinson's unexpected action was not immediately clear.

Nearly all the 160,000 UMW strikers have been ignoring the order anyway, and the government had made no attempt to enforce it with contempt-of-court citations. But there has been a significant increase in production of nonunion coal since the one-week order came down banning any form of interference with the mining or transportation of coal.

Meanwhile, union members are scheduled to vote next Friday on a new contract major industry concessions on wildcat strike controls and health and pension benefits, which were the main obstacles to ratification of a previously negotiated contract.

The Justice Department sought to extend the temporary order until March 28 on grounds that an extension would be less disruptive to the contract ratification process than a full-scale injuction.

Yesterday's hearing before Robinson had originally been scheduled for arguments on the injuction.

The government has the support of the coal industry for the extention. And the UMW, while urging dismissal of the temporary order, told the court it wuold have "no objection" to an extention that delayed an injunction beyond the contract referendum dater.

However, attornets, for several UMW districts and for the American Civil Liberties Union argued that there was no legal basis for extending the order and contended that no order at all would have the least disruptive effect on the contract voting.

Let the order expire and permit the miners to vote "as free Americans," argued ACLU attorney Joseph L. Rauh.

"They're not paying attention to what I'm doing anyway," retorted Robinson.

Displaying impatience at the government's lack of evidence and lack of zeal in enforcing his earlier order. Robinson made it clear almost from the strat of the hearing that the government could not prove to his satisfaction that a national emergency exists, as required under the Taft-Hartley Act for a strike-ending order.

Robinson said he based his March 9 order on President Carter's contention that an emergency existed. But later he studied more carefully the government's affidavits in support of the temporary order, many of which were signed by Cabinet members and found them "not relevant," the judge declared.

Only three of the 11 affidavits warned of risk to the "national health and safety," as the Taft-Hartley Act requires, said Robinson, and those three "had to be stretched" to reach that conclusion.

The voluminous affidavits citied such coal strike results as suspension of hot lunches in school cafeteries, death from a cutoff of electric power to traffic lights, and threats to the nation's foreign policy and defense posture.

They warned that as many as 3 miilion workers might be laid off because of the strike by mid-April, although Labor Department reports have subsequently shown a slight decline in strike-related layoffs, which now number about 22,000.

When Justice Department attorney Glenn V. Whitaker said the government was prepared to go ahead with arguments based on the affidavits,Robinson retorted: "If you want to stand on that you could be in the Court of Appeals tomorrow," implying he would rule immediately against an injuction request based on existing evidence.

Robinson also asserted that the government has shown no inclination to enforce the temporary order over the last seven days and said he had "no intention" of issuing any more orders that weren't going to be enforced.

Whitaker insisted that the government was proceeding with enforcement of the order by issuing instructions to law enforcrment officials and calling in the FBI to investigate possible violations. "Our intention was not delay . . .," said Whitaker, adding that the government still contends that a national emergency exists and wants an injuction.

H. John Rogers, an attorney for several locals in Ohio's UMW District 6, said "I am absolutely and totally nonplussed that the government would seek an extention of an order it has not bothered to enforce." He charged that the goverment was holding the threat of an 80-day injuction, under which food stamps and possibly other welfare benefits would be cut off, as a "sword of Damocles" over the heads of miners as they prepare to vote on a contract.

In his written order rejecting the proposed extention, robinson agreed to put off arguments on the injuction until after the voting, as the government requested, but said the government had not shown "good cause" for extension of the temporary order. "Absent additional evidence of irrparable harm to the national health or safety of the United States . . . this court must deny the government's request," said the judge.