* Milder weather predictions pressure prices * Texas and the South expect warm mid- to late-June * Coming up: EIA's short-term energy outlook Tuesday By Joe Silha NEW YORK, June 10 (Reuters) - U.S. natural gas futures ended lower on Monday, with the slightly milder trend in computer weather forecasts and expectations for another big inventory build driving the front contract to a three-month low. "We saw some early gains but they couldn't hold. I think the big inventory build last week still has some people spooked, and there's just not enough heat in the forecast right now," said Kyle Cooper, managing partner at IAF Advisors in Houston. Front-month gas futures on the New York Mercantile Exchange ended down 2.8 cents at $3.80 per million British thermal units after climbing early to $3.868, then sinking to a three-month low of $3.779. The front contract, which lost nearly 10 percent in the previous two weeks, has posted a fresh three-month low in each of the last three sessions. Technical traders noted the chart turned bearish late last week after prices dropped below support in the $3.90 area. Although prices on Monday briefly breached next support at the 100-day moving average at $3.80, traders noted the front month closed at that level, casting doubts about the next move. Texas and parts of the South were still expected to warm up later this week and next week, but many traders remain skeptical of the upside without a broader-based heat wave to stir demand. AccuWeather.com expects temperatures in the major gas consuming region of the Northeast United States to remain near normal for the next week. Readings in the Midwest, another big gas using region, will mostly average below seasonal temperatures during the period. Prices attempted to move up early Monday, but traders agreed high production and worries about the potential for another big inventory build on Thursday were keeping buyers nervous. Early injection estimates for this week's Energy Information Administration storage report range from 90 to 112 billion cubic feet, well above the 66-bcf build seen during the same week last year and the five-year average increase for that week of 84 bcf. Baker Hughes data on Friday showed the gas drilling rig count at 354 was still hovering just above an 18-year low, but U.S. gas production in 2013 has not slowed much, if at all, from last year's record highs. Traders were waiting for more clues on production when EIA releases its short-term energy outlook on Tuesday.