Explanation:

The following program contains two classes. 
•    Temperature class
•    TemperatureTest class

The Temperature class contains two instance variables, four constructor methods, two accessor methods to return the temperature and scale, three mutator methods, three comparison methods and a suitable toString() method.
The TemperatureTest is used to test the Temperature class. The TemperatureTest class contains objects of Temperature class. The Temperature class methods are used in this method. This includes at least one true and one false case for each of the comparison methods.
 

Code:

/*********** Filename: Temperature.java ***********/

// Create a class named Temperature.
public class Temperature
{
	// Declare the two instance variables.
	private double temperature;
	private char scale;
	
	// Create four constructor methods.
	// Create a no-argument constructor.
	public Temperature()
	{
		// Set to zero degrees Celsius.
		temperature = 0;
		scale = 'C';
	}
	
	// Create a constructor for the instance variable named scale.
	public Temperature(char scale)
	{
		this.scale = scale;
		// Assume zero degrees if no value is specified.
		temperature = 0;
	}
	
	// Create a constructor for the instance variable named temperature.
	public Temperature(double temperature)
	{
		this.temperature = temperature;
		// Assume Celsius, if no scale is specified
		scale = 'C';
	}
	
	// Create two parameters constructor for the two instance variables.
	public Temperature(double temperature, char scale)
	{
		this.temperature = temperature;
		this.scale = scale;
	}
	
	/********** (1) **********/
	
	// Create two accessor methods.
	// Create an accessor to return the degrees Celsius.
	public double getCelsius()
	{
		if (scale == 'C')
		{
			return temperature;
		}
		else
		{
			// Round to the nearest tenth of a degree
			return ((double) (Math.round((5 * (temperature - 32.0) / 9.0) * 10.0)) / 10);
		}
	}
	
	// Create an accessor to return the degrees Fahrenheit
	public double getFahrenheit()
	{
		if (scale == 'F')
		{
			return temperature;
		}
		else
		{
			// Round to the nearest tenth of a degree
			return (Math.round((9 * (temperature / 5) + 32) * 10) / 10);
		}
	}
	
	/********** (2) **********/
	// Create three mutator methods.
	// Create a mutator to set the temperature.
	public void setTemperature(double temperature)
	{
		this.temperature = temperature;
	}
	
	// Create a mutator to set the scale
	public void setScale(char scale)
	{
		this.scale = scale;
	}
	
	// Create a mutator to set both
	public void setTemperatureScale(double temperature, char scale)
	{
		this.temperature = temperature;
		this.scale = scale;
	}
	
	/*********** (3) *********/
	// Create three comparison methods.
	// Create an equals method to test whether 
	// two temperatures are equal or not.
	public boolean equals(Object obj)
	{
		if (obj instanceof Temperature)
		{
			Temperature t = (Temperature) obj;
			return getCelsius() == t.getCelsius();
		}
		return false;
	}
	
	// Create a method to test whether one temperature is greater than another.
	public boolean lessthan(Object obj)
	{
		if (obj instanceof Temperature)
		{
			Temperature t = (Temperature) obj;
			return getCelsius() > t.getCelsius();
		}
		return false;
	}
	
	// Create a method to test whether one temperature is less than another.
	public boolean greaterthan(Object obj)
	{
		if (obj instanceof Temperature)
		{
			Temperature t = (Temperature) obj;
			return getCelsius() < t.getCelsius();
		}
		return false;
	}
	
	/************ (4) ***********/
	// Create a suitable toString method.
	public String toString()
	{
		if (scale == 'C')
		{
			return String.format("%.1f degrees C = %.1f degrees F", temperature, getFahrenheit());
		}
		else
		{
			return String.format("%.1f degrees F = %.1f degrees C", temperature, getCelsius());
		}
	}
}

/*********** Filename: TemperatureTest.java ***********/

// Create a class named TemperatureTest
public class TemperatureTest
{
	// Create a main method to run the program.
	public static void main(String[] args)
	{
		System.out.println("Celsius to Fahrenheit:");
		
		// Create an object named c2fObj1.
		Temperature c2fObj1 = new Temperature();
		c2fObj1.setTemperature(0.00);
		c2fObj1.setScale('C');
		System.out.println(c2fObj1.toString());

		// Create an object named c2fObj2.
		Temperature c2fObj2 = new Temperature('C');
		c2fObj2.setTemperature(-40);
		System.out.println(c2fObj2.toString());
		
		// Create an object named c2fObj3.
		Temperature c2fObj3 = new Temperature(100.00, 'C');
		System.out.println(c2fObj3.toString());
		
		// Create an object named f2cObj1.
		System.out.println("\nFahrenheit to Celsius:");
		Temperature f2cObj1 = new Temperature(0);
		f2cObj1.setTemperatureScale(56.00, 'F');
		System.out.println(f2cObj1.toString());
		
		// Display Comparision.
		System.out.println("\nComparision:");
		System.out.println("c2fObj1 < c2fObj2: " + c2fObj1.lessthan(c2fObj2));
		System.out.println("c2fObj2 = c2fObj3: " + c2fObj1.equals(c2fObj3));
		System.out.println("c2fObj3 > f2cObj1: " + c2fObj3.greaterthan(f2cObj1));		
	}	
}

Output:

Celsius to Fahrenheit:
0.0 degrees C = 32.0 degrees F
-40.0 degrees C = -40.0 degrees F
100.0 degrees C = 212.0 degrees F

Fahrenheit to Celsius:
56.0 degrees F = 13.3 degrees C

Comparision:
c2fObj1 < c2fObj2: true
c2fObj2 = c2fObj3: false
c2fObj3 > f2cObj1: false