* Futures bounce ahead of weekly inventory data Thursday * High inventories, production limit upside in prices * Milder forecast for next week keeps buyers cautious * Coming up: EIA storage and gross gas production data Thursday By Joe Silha NEW YORK, Jan 30 (Reuters) - Front-month U.S. natural gas futures closed higher on Wednesday for the first time in seven sessions on buying ahead of Thursday's weekly inventory report and in reaction to an expected increase in demand as forecasts call for colder weather over the next few days. "Prices are tentatively higher today with a bit more cold being put back into U.S. weather forecasts," Gelber & Associates analyst Aaron Calder said in a report. Calder also noted that traders were likely pricing in expectations for a big inventory draw on Thursday that should be the largest of the heating season so far. But most traders expect only limited upside from this next cold shot, focusing instead on concerns that the back half of winter may not turn out cold enough to whittle down high inventories amid record production. Front-month gas futures on the New York Mercantile Exchange ended up 7.7 cents, or 2.4 percent, at $3.335 per million British thermal units after trading between $3.261 and $3.344. The front contract, which hit a 6-1/2-week high of $3.645 early last week, lost 9.5 percent in the previous six sessions, its biggest six-day slide in nearly seven weeks. The sell-off helped turn the technicals bearish, but some chart watchers said the market was oversold and due for a bounce, particularly ahead of what should be a very bullish weekly inventory report on Thursday. In its Wednesday report, MDA Weather Services noted that the Great Lakes to Northeast regions will likely to turn cold in the middle of the six-to-10-day period before the next round of warmth arrives later next week. The private forecaster also noted that the 11-to-15-day forecast continued to favor warmer for the eastern half of North America, keeping heating demand below normal during the period. ANOTHER BIG STORAGE DRAW EXPECTED Weekly inventory draws have topped market expectations for four straight weeks and that trend may continue in Thursday's U.S. Energy Information Administration storage report. Traders and analysts polled by Reuters expect inventories to have fallen by 206 billion cubic feet (bcf) last week, which would be the biggest draw of the heating season so far and the largest weekly decline in about two years. Stocks fell an adjusted 149 bcf during the same week last year. The five-year average decline for that week is 178 bcf. But despite recent strong storage pulls, traders noted that stocks are still relatively high at 320 bcf, or 12 percent, above the five-year average. If drawdowns for the rest of winter match the five-year average, inventories will end March at 2.048 trillion cubic feet, 18 percent above normal but 17 percent below last year, when stocks finished a very mild heating season at a record-high 2.48 tcf. GAS RIG COUNT GAINS, FIRST TIME IN 3 WEEKS The Baker Hughes gas-directed drilling rig count gained last week for the first time in three weeks. The overall count at 434 is not far above the 13-1/2-year low of 413 posted in early November, but so far production has shown no significant sign of slowing. The EIA estimates that gas output in 2013 will hit a record high for the third straight year.