So I built an IR receiver using this: http://www.vishay.com/docs/82013/tsop12xx.pdf

where an LED lights up once an infrared signal is given, which worked perfectly. Now I want to replace the LED with a 1.5-3V basic motor: http://www.radioshack.com/product/index.jsp?productId=2102822

However, the motor does not work. And if I use a 9V battery, the receiver module heats up and the motor runs continuously. How can I make the motor run with the infrared signal?

 

The datasheet you linked clearly says the max output current for your receiver is 5mA, which is not enough for a motor. You need an external PNP transistor with a pullup resistor to Vcc on its base pin, which will also connect to the receiver output. Drive the motor by a connection to ground and the power line connected to the emitter. Collector to Vcc.

 

You need to buffer the output with a transistor, replace the buzzer for your motor.

buffer use a 1K resistor for R3, and omit R2.