The record-breaking heat wave of July and August helped pushed electric bills up nearly 13 percent for customers of Potomac Electric Power Co.

The average customer's bills for July and August climbed to a total of $147.85 from last year's level of $130.96--a 12.9 percent increase, according to figures supplied by Pepco.

But the worst may be yet to come this month when customers receive their September bills, Pepco officials say. These bills could be far higher because they will reflect the electricity consumed during late August and early September, when temperatures frequently hovered near the 100-degree mark.

For July and August alone, temperatures reached or exceeded 90 degrees on 37 days--more than double the number in 1982.

The weather was so hot, in fact, that demand for air conditioning broke two records in July, with Pepco supplying 4,283 megawats in its peak hour. With Pepco's net generating capacity totaling 5,400 megawats, the utility still had room to spare, however.

Virginia Electric Power Co. also experienced a sharp increase in electricity demand, up 12.1 percent from last year. But Vepco did not have exact statistics on how much an average bill increased.

According to Pepco's figures, the average residence consumed 12.3 percent more electricity during July and August than it did during the same two months last year, from 1,810 to 2,033 kilowatts for the two months.

For Maryland customers, that increase translated into an 8.6 percent higher electric bill--$169.30 compared with $155.88 last year. The increase would have been higher had it not been for two rate reductions Pepco made to account for a decrease in the utility's fuel costs.

District of Columbia residents saw a far higher increase--24.8 percent--over last year, with the average bills for July and August totaling $112.16, compared with $89.85 last year. Bills for District residences are smaller than Maryland homes because the houses are smaller, Pepco said.

Pepco's 3,500 Virginia customers--most of whom live in small apartments--saw a 10.8 percent increase in their July and August bills, from $66.42 to $73.59.

Systemwide, Pepco says the average bills totaled $147.85 for July and August, up $16.89 from last year.

Pepco officials note that June's rainy period helped to keep summer electric bills down, accounting for a 2.2 percent decrease in the average Pepco bill for that month.