B737 Captain reports encountering unforecast convective weather upon arrival at MIA. Runway 9 is requested for landing and windshear is encountered at 1;000 FT during approach. A normal landing ensues.

Narrative

Flight plan had Alternate NONE with a one hour and thirteen minute planned arrival fuel. I noted the flight plan weather for MIA had only a 30% chance of precipitation and no mention of convective weather; the SA hourly report had 10 SM visibility with -RA. Having left MIA just a few hours ago with numerous showers around I called to question this with the Dispatcher. He said the weather was dissipating and should be fine for our arrival with just a few storms en route over the mid-Atlantic. When we were on the descent into MIA the radar began to show a large storm over FLL with LTICCG (lightning in cloud and cloud to ground). We were vectored for an ILS approach to 08R. The weather was building rapidly and extending to the MIA airport. We heard a report of a 15 KT loss by another flight that had just landed 08R. I instructed the First Officer to tell the Tower we would need Runway 09; longer; full ILS minimums; and no report of wind shear for that runway. We were in a position of minimum fuel if a go-around and divert would be necessary due not having a filed alternate and the corresponding fuel. FLL the closest airport was not an option due to the storm over MIA-FLL. We checked with the Tower and the runway conditions appeared dry to them and the visibility at the surface was still 10 SM. We had a windshear encounter at about 1;000 FT. After our arrival and a departure and subsequent arrival the Tower changed to a west flow. It must be stressed that the Commercial Weather Forecast had NO CONVECTIVE WEATHER in its amended forecast.