1995 Buick Skylark Heating problem

My car runs about fifteen minutes, and my temperature gauge only moves a little from the cold mark. The cars warms up. Once I start driving the gauge needle goes back to C and and cold air comes out.I drive 22 miles to work and the car never runs hot or never blows out any heat. My thermostats is not located on the top the engine I cannot find it They say it is in the water pump. Their is know leakage in the car so my heater core is find. And theirs is know leak in my radiator. My coolant stays full. Can you help me out thanks