In Actionscript I'd use an array and push() and pop(), but I'm not sure there are equivalent array methods in Processing/Java...

One option might be to create a simple class to hold the temp data (must admit I'm not 100% sure this step is necessary).  Anyway you could then use an ArrayList in which to store your data.  You can then simply use add to append data to the ArrayList as it comes in.  Once your array grows to the full width of the graph (just a simple test against the length of the ArrayList) you would then just use remove to remove the first element, before appending the next bit of data to the end.

Once you have that structure in place it's just a matter of iterating through the ArrayList, retrieving the temp data and plotting it to the graph...

It may of course be that there's a simpler option, but I reckon the logic is sound.  A similar approach is used to smooth data with an arduino, and it may be that their example code might offer another solution.

I don't have a device on the serial port, so I will simulate the data:
Code:

int numberOfGraphPoints=1200; 
float[] tempValsA = new float[numberOfGraphPoints]; // initialize 1st array
float[] tempValsB = new float[numberOfGraphPoints]; // initialize 2nd array
int currentPoint=0; // the marker used to travel through the array.
//Serial commPort;
int previousGrabTime=0, timeStep=10; // low timestep for fast demo
float tempC;
float tempF;
float tempB;
float tempEnvF;

void setup(){
  size(800,600);
  background(255); // white
  currentPoint=0; // reset array marker
//  commPort = new Serial(this, Serial.list()[1], 9600);
}

float prevTemp = 20; // Just for simulation
void draw()
{
//  while (commPort.available() > 1)
  {
//    tempC = commPort.read();
//    tempB = commPort.read();
tempC = prevTemp + random(-0.5, 0.5);
prevTemp = tempC;

    // converts tempC to Fahrenheit
    tempF = ((tempC * 9) / 5) + 32;
    // converts tempB to Fahrenheit
    tempEnvF = ((tempB*9)/5) + 32;
  }

  if (currentPoint < numberOfGraphPoints){ // don't exceed your arrays
    if (millis() - previousGrabTime >= timeStep){ // if it's time to grab
	// grab the values for A and B
	// store them in the two float[] arrays
	tempValsA[currentPoint] = tempF; // plug the values into the arrays
	
	float x = map(currentPoint, 0, numberOfGraphPoints, 0, width);
	float y = map(tempF, 0, 375, height, 0);
	 
	stroke(0);
	point(x, y);
	
	currentPoint++; // add 1 to the current point
	previousGrabTime = millis(); // reset the wait time
    }
  }
}
 

You have already the previous temp, since you store them in an array (not really using it, currently, but it will come later). So the change is simple:
Code:

	float x = GetX(currentPoint);
	float y = GetY(tempF);
	float px = GetX(currentPoint - 1);
	float py = GetY(tempValsA[currentPoint - 1]);
	 
	stroke(0);
	line(px, py, x, y);
 

I have put the code to map points in functions to avoid duplication of code:
Code:

float GetX(float v)
{
  return map(v, 0, numberOfGraphPoints, 0, width);
}
float GetY(float v)
{
  return map(v, 0, 375, height, 0);
}
 

And I start currentPoint at 1...
Well, actually there is a simpler method, with less computation, making px and py global and assigning them to x and y before changing the latter...

well that was easy.  Thank you both.  However, I have a red vertical line, spanning the height of the screen.  Just at the very beginning.

Is there a way to get a thicker line? // nevermind just added strokeWeight(3);  

Code:

import processing.serial.*;

int numberOfGraphPoints=1200; // match width for simplicity in demo
float[] tempValsA = new float[numberOfGraphPoints]; // initialize 1st array
float[] tempValsB = new float[numberOfGraphPoints]; // initialize 2nd array
int currentPoint=0; // the marker used to travel through the array.
int currentPointA=0;
int maxTemp = 375;
int minTemp = 0;

Serial commPort;
int previousGrabTime=0, timeStep=1000; // low timestep for fast demo
float tempC;
float tempF;
float tempB;
float tempEnvF;
float x,y,px=0,py=0;
float xa,ya,pxa=0,pya=0;



void setup(){
  size(800,600);
  background(255); // white
  currentPoint=0; // reset array marker
  commPort = new Serial(this, Serial.list()[1], 9600);
}

void draw()
{
while (commPort.available() > 1)
{
tempC = commPort.read();
tempB = commPort.read();
// removed draw graph and placed in new procedure drawgraph()
// draw graph sets up graph area but doesn't plot data
tempF = ((tempC * 9) / 5) + 32;
// converts tempC to Fahrenheit
tempEnvF = ((tempB*9)/5) + 32;
// converts tempB to Fahrenheit
}



  if (currentPoint < numberOfGraphPoints){ // don't exceed your arrays
    if (millis() - previousGrabTime >= timeStep){ // if it's time to grab
	
	// grab the values for A and B
	// store them in the two float[] arrays
	
     
     float x = map(currentPoint,0,numberOfGraphPoints,0,width);
     float y = map(tempF,minTemp,maxTemp,height,0);
     float xa = map(currentPointA,0,numberOfGraphPoints,0,width);
     float ya = map(tempEnvF,minTemp,maxTemp,height,0);
     
 
	tempValsA[currentPoint]=tempF; // plug the values into the arrays
     
	
	currentPoint++; // add 1 to the current point
	currentPointA++;
	previousGrabTime = millis(); // reset the wait time
	 
	 stroke(0);
     line (px,py,x,y);
   px = x;
   py = y;
   stroke(255,0,0);
     line (pxa,pya,xa,ya);
     pxa=xa;
     pya = ya;
    }
  
  }
}
 

OK.  I guess I'm keeping a dialogue with myself.  Which is good.  But I was able to fix the problem.  I just drew boxes over the text, so they dont flash, which also covered the line from 0,0 to starting temp.  It works great now.  
Next step is to make the graph start to plot when the timer is started.  And then freeze when timer is stopped.