* Chilly near term forecasts underpin price gains * Growing supplies, milder midmonth outlook limit upside By Joe Silha NEW YORK, Nov 8 (Reuters) - U.S. natural gas futures ended higher for a fourth straight day on Friday, backed by chilly weather forecasts for the eastern half of the country over the next 10 days that should force more homeowners and businesses to turn up their heaters. Front-month futures, which posted a contract low and 2-1/2 month low of $3.379 per million British thermal units on Tuesday, gained 3.3 percent in the last four sessions and finished the week up 1.3 percent. It was the first weekly rise for the nearby contract in four weeks. "The market got overextended to the downside last week, but the weather forecast doesn't look as bearish this week," said Steve Mosley at The SMC Report, noting last week's 5.2 percent slide was the largest weekly decline in two months. Many traders remained skeptical of the upside despite this week's gains, with stockpiles comfortable, production flowing at a record high pace and another warm-up expected late next week, particularly for the Midwest. Front-month gas futures on the New York Mercantile Exchange ended up 4 cents, or 1.1 percent, at $3.559, after trading between $3.51 and $3.589. MDA Weather Services expects below normal temperatures to dominate the eastern half of the United States for the next 10 days. But the forecaster does expect milder readings in its 11-to-15-day outlook, particularly for the Midwest and Southwest. Traders mostly shrugged off Thursday's 35 million cubic feet weekly inventory build, noting it matched the Reuters poll estimate and came in close to the five-year average for that week. Most viewed the injection as neutral for prices. The U.S. Energy Information Administration reported that total gas inventories rose last week to 3.814 trillion cubic feet, 2.9 percent below last year's record highs at that time but 1.5 percent above the five-year average. Early injection estimates for next week's storage report range from 16 bcf to 36 bcf. That would compare to a 12 bcf draw during the same year-ago week and the five-year average increase of 19 bcf for that week. Baker Hughes data showed that the gas drilling rig count rose this week for the third time in four weeks, gaining five to 365. The gas rig count has risen in 12 of the last 20 weeks. A rising gas rig count can stir talk that new pipelines and processing plants, particularly in the East, may be encouraging producers to hook up more wells and pump more supply into an already well-supplied market. The EIA still expects U.S. gas production in 2013 to hit a record high for the third straight year. In the ICE cash market, gas for weekend delivery at Henry Hub , the benchmark supply point in Louisiana, slipped 3 cents to $3.54, with late differentials weakening to about 6 cents under NYMEX from a 3-cent discount on Thursday. Gas on the Transco pipeline at the New York citygate tumbled 24 cents to $3.35 despite the chilly outlook, undermined by the typical drop in weekend demand. Chicago was 8 cents lower at $3.66. For daily ICE U.S. cash gas prices, click on .