* Warmer trend this week lifts prospects for demand * Front-month futures end up for second day By Joe Silha NEW YORK, May 20 (Reuters) - U.S. natural gas futures ended higher for a second straight session on Monday as warmer weather stretching from Texas to the Northeast this week should boost demand by forcing homeowners and businesses to crank up their air conditioners. Prices have bounced roughly 4 percent in the last two trading sessions as forecasts finally started to trend warmer. Commodity Weather Group said it expected the most humid air of the season so far to move into the Midwest and East this week, offering some uncomfortable heat index levels. While the forecaster sees heat lingering in the Midwest for the next two weeks, mostly seasonal temperatures were expected for the East, Gulf Coast and West in its six- to 10-day outlook. "Today's rise looks to be weather driven. Current weather reports show a shift to warmer-than-normal weather, indicating the beginning of summer cooling demand," Gelber & Associates analyst Aaron Calder said in a report. Front-month gas futures on the New York Mercantile Exchange ended up 3.5 cents at $4.09 per million British thermal units after trading between $4.063 and $4.159. But gains in deep deferred contracts far outpaced the rise in the front months, with most 2018 contracts ending about 13 cents higher on news Friday that the U.S. Energy Department had approved natural gas exports from Freeport LNG's Texas terminal. Traders noted the liquefaction plant will take several years to build but could help tighten the supply-demand balance later this decade. Chart traders noted the market seemed well supported in the $3.90s after testing and holding that area several times last week. But with supplies still comfortable, many traders remain skeptical of the upside, at least until a broader-based heat wave forces more air conditioning loads. COMFORTABLE PRODUCTION, STORAGE Baker Hughes data Friday showed the gas-directed rig count climbed last week by four to 354 after posting an 18-year low last week. Despite a steep decline in dry gas drilling over the last year and a half, production has not slowed much, if at all. The Energy Information Administration still expects output in 2013 to post a record high for a third straight year. Inventory builds have exceeded market expectations for three straight weeks as mild May weather slowed overall demand. Early injection estimates for Thursday's EIA storage report range from 87 billion to 99 billion cubic feet versus a 75-bcf build during the same week last year and a five-year average rise for that week of 90 bcf.