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I must be using the wrong transistor for a 12 volt dc motor because it is heating up. 
It's an NPN TIP3055 transistor.
power dissipation: 75 W
Collector-emitter voltage: 60 V
collector - base voltage: 70 V
emitter-base voltage 5 V
collector current: 10 A

What kind of numbers should I have on a transistor?
I'm wiring it like the first schematic here: http://www.thebox.myzen.co.uk/Workshop/Motors_1.html
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I must be using the wrong transistor for a 12 volt dc motor because it is heating up.

That is not always terrible. How hot? Can you keep your finger on it?

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What kind of numbers should I have on a transistor?

It very much depends upon the numbers you have on your motor! How much current does it draw at 12V?

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A mosfet would be my first choice.

The hfe (amplification) of the TIP3055 is low for high currents. Are you sure it gets enough current at the base ?
A darlington is also often used, but those get hotter, because of the voltage drop.
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How much current does it draw at 12V?
I'm pretty sure it draws 2 amps of current based on similar looking motors online.  It was taken off a Mattel car that kids can drive around in.  I have another one like it taken off of an electric tire pump. 

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Are you sure it gets enough current at the base ?
I've giving it 5 volts from the arduino.

What numbers should I look for on a mosfet if I go with that?
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2A / 50 = 40mA
That is the maximum what the Arduino can handle.
To get the transistor to be fully on, about 30% extra current is used. So the transistor is getting hotter than it should be.

You forgot to mention what the value of the resistor is, between the Arduino and the base of the transistor.

A mosfet could be RFP12N10L, but most power logic mosfet will do.
It has to be a logic mosfet, because normal mosfets are 'on' at about 9V, and the mosfet should be 'on' if the pin of the Arduino is between 4 and 5V.
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I have the RFP12N10L mosfet but I am encountering a problem.  It is staying constantly on.  I am wiring it like the first schematic on this page:  http://www.thebox.myzen.co.uk/Workshop/Motors_1.html 
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I have the RFP12N10L mosfet but I am encountering a problem.  It is staying constantly on.  I am wiring it like the first schematic on this page:  http://www.thebox.myzen.co.uk/Workshop/Motors_1.html 
That shows a circuit using an NPN.  Assuming that you are equating Gate for Base, Source for Emitter, and Drain for Collector, there's one thing missing: a resistor.  The Gate has a capacitance, it stores a charge and it stays there when the gate is biased off; add a 10K resistor from gate to Ground to bleed off that charge.  Use a value < 1K (220-330Ω?) for the present "3.3K" resistor.
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