Questar Corp. reported earnings of $26.93 million, or $1.38 per share, in the first quarter of 1988 compared with $19.55 million, or $1.10 per share, for the year-ago period.

Questar, parent company of Mountain Fuel Supply Co. and other energy subsidiaries, said the first quarter results reflected colder weather that increased natural gas deliveries and new rates for the company's natural gas transmission operations.The year-earlier quarterly total included a $9 million, or 48 cents per share, after-tax write-down of oil and gas properties under the full-cost accounting method. Excluding the write-down, the 1987 net income figure would have been $28.55 million, or $1.58 per share.

Questar had 19.29 million average shares of common stock outstanding during first quarter 1988 compared with a 17.45 million a year ago. The company issued 1,725,000 shares of common stock in June 1987.

Mountain Fuel earned $15.59 million during the 1988 period compared with $13.69 million a year earlier. Temperatures in the utility's service area were 3 percent colder than normal and 8 percent colder than during the year-ago quarter, helping boost deliveries to residential and commercial customers by 7 percent.

Industrial deliveries increased 25 percent principally because of the return of several major customers. Total deliveries increased 11 percent to 42.4 million decatherms.

"The return of more-normal weather and higher deliveries for our gas distribution and transmission operations, along with the avoidance of write-downs in our exploration and production business, are encouraging signs," said Questar Chairman R.D. Cash.

"Conditions are still difficult for the energy business, but we are confident that they are beginning to improve."