Instead of calculating the time taken to heat a mass of soil, I opted for a real world test. In order to test the capability of the 5W PCB heater two TMP36 temperature sensors were used in conjunction with a Arduino Uno and minimal serial output. Adafruit has a nice overview of how to use the TMP 35/36 series of temperature sensors at:  

https://learn.adafruit.com/tmp36-temperature-sensor

Again taking from the simple examples at Adafruit a simple comma separated values stream was created for viewing in the serial monitor. The analogue pins of the TMP36 were wired to AN0 and AN1.

Code Snippet:

/*
 * initialize the serial connection
 */
void setup()
{
  Serial.begin(9600);  //Start the serial connection 
                       //to view the temperature open the serial monitor
}
int twoSeconds = 0; 
void loop() 
{
 //getting the voltage reading from the temperature sensor
 int reading1  = analogRead(0);  
 int reading2  = analogRead(1); 
//conversion from reading to voltage
 float voltage1 = reading1 * 5.0;
 voltage1 /= 1024.0; 
 //converting from 10 mv per degree with 500 mV offset
 float temp1 = (voltage1 - 0.5) * 100 ;  
 
 float voltage2 = reading2 * 5.0;
 voltage2 /= 1024.0; 
 float temp2 = (voltage2 - 0.5) * 100 ;
 twoSeconds++;
 //comma separated output
 Serial.print(twoSeconds);Serial.print(" , ");
 Serial.print(temp1);Serial.print(" , ");
 Serial.print(temp2);Serial.print("\n");
 //waiting a 2 seconds
 delay(2000);                  
}

The PCB heater was then provided with 5V giving a power dissipation of around 5W. No feedback is given at this stage to the heating element, just open loop at 5W. The heater was placed under ~40mm of soil with one sensor directly attached to the heater and the other on top of the soil. The picture below gives away my plans for a low cost propagator housing with universal availability and passive watering. 

The bottle steamed up nicely as the heat increased inside.

After copying the serial monitor output of the Arduino IDE to a text file and importing it into a spreadsheet this graph was generated.

At this early stage a 5W heater is looking feasible to heat around 450g of moist soil or potting compound within an hour or two. The heater temperature is too high currently an will have to be reigned in with some basic bang bang feedback which will slow the heating of the soil down but create a better environment for the plants root system overall. At around 40 minutes I moved soil temperature probe to a distance of ~50mm from the heater hence the transient.

Next up, really simple bang bang control and closing the loop!