* Forecasts turn cooler for most of eastern U.S. * Warmer weather still expected to move into the Northeast By Joe Silha NEW YORK, June 28 (Reuters) - U.S. natural gas futures ended lower on Friday, with mild weather forecasts for most of the eastern half of the nation next week driving the front contract to a 3-1/2 month low despite expectations for some record heat out West. "The early July temperature forecast looks very bearish for next week. It shows cooler air moving into the central U.S.," said Steve Mosley at The SMC Report in Arkansas. Traders said recent bearish weekly inventory reports also triggered some selling, noting prices sold off more than 4 percent on Thursday after the Energy Information Administration reported that stocks climbed last week by 95 billion cubic feet. That was well above market expectations of 88 bcf and the five-year average gain for that week of 79 bcf. Inventory builds have exceeded the five-year average for the last four weeks and prompted some analysts to raise estimates for peak storage this year. But most still expect stocks to head into next heating season below last year's record high. Front-month gas futures on the New York Mercantile Exchange ended down 1.7 cents at $3.565 per million British thermal units after slipping early to a 3-1/2 month low of $3.526. The front contract, which fell 5.5 percent this week, finished the month 10.5 percent lower. For the second quarter, the contract logged an 11 percent loss though it is still up about 6 percent so far this year. Heat remains focused in the West for the next two weeks, but temperatures were also expected to trend warmer for the Northeast and the upper Midwest during the period, according to forecaster MDA Weather Services. Readings in the central and southeast states were expected to average below normal. With gas inventories only slightly below average for this time of year and production still flowing at or near a record peak, many traders expect prices to remain on the defensive until a broader-based heat wave arrives and kicks up demand. Baker Hughes data on Friday showed the gas drilling rig report rose this week by four to 353 after posting an 18-year low the previous week. Despite the slowdown in gas drilling over the last 20 months, EIA expects gas output in 2013 to post a record high for a third straight year.