More details on the circuit here: http://publiclab.org/notes/donblair/05-28-2014/riffle-dev-fun-w-five-five-fives

dwbConductivityTempLowPower.ino

#include <JeeLib.h>

 ISR(WDT_vect) { Sleepy::watchdogEvent(); }


long pulseCount = 0;  //a pulse counter variable

unsigned long pulseTime,lastTime, duration, totalDuration;

int samplingPeriod=2; // the number of seconds to measure 555 oscillations

int fivefivefive = 13; // the pin that powers the 555 subcircuit


int sensorPin = 0; // the analog pin from which we'll make a temp measurement
// https://learn.adafruit.com/tmp36-temperature-sensor

void setup()
{
  Serial.begin(9600);
  
      pinMode(fivefivefive, OUTPUT);   
           
}

void loop()
{
  
  Serial.println("yawn ...");
  
  Serial.flush(); // this and next line for serial printouts only -- need to make sure serial flushed before sleeping
  delay(2);

  Sleepy::loseSomeTime(5000); // sleeping
 
  delay(2); //for serial printouts only -- need to ensure uController woke up before printing
  
  
  Serial.println("-- good morning!");
  
  // now make a temp measurement
  
  int reading = analogRead(sensorPin);  
 
 // converting that reading to voltage, for 3.3v arduino use 3.3
 float voltage = reading * 3.3;
 voltage /= 1024.0; 
 
 // print out the voltage
 //Serial.print(voltage); Serial.println(" volts");
 
 // now print out the temperature
 float temperatureC = (voltage - 0.5) * 100 ;  //converting from 10 mv per degree wit 500 mV offset
                                               //to degrees ((voltage - 500mV) times 100)
 Serial.print(temperatureC); Serial.println(" degrees C");
 
 
  // now make a conductivity measurement
  
  //turn on the 555 system
  digitalWrite(fivefivefive,HIGH); //turns on the 555 timer subcircuit
  
  pulseCount=0; //reset the pulse counter
  totalDuration=0;  //reset the totalDuration of all pulses measured
  
  attachInterrupt(1,onPulse,RISING); //attach an interrupt counter to interrupt pin 1 (digital pin #3) -- the only other possible pin on the 328p is interrupt pin #0 (digital pin #2)
  
  pulseTime=micros(); // start the stopwatch
  
  delay(samplingPeriod*1000); //give ourselves samplingPeriod seconds to make this measurement, during which the "onPulse" function will count up all the pulses, and sum the total time they took as 'totalDuration' 
 
  detachInterrupt(1); //we've finished sampling, so detach the interrupt function -- don't count any more pulses
  
  //turn off the 555 system
  digitalWrite(fivefivefive,LOW);
  
  if (pulseCount>0) { //use this logic in case something went wrong
  
  double durationS=totalDuration/double(pulseCount)/1000000.; //the total duration, in seconds, per pulse (note that totalDuration was in microseconds)
  
  // print out stats
  Serial.print("sampling period=");
  Serial.print(samplingPeriod);
    Serial.print(" sec; #pulses=");
  Serial.print(pulseCount);
  Serial.print("; duration per pulse (sec)=");
  Serial.println(durationS,5);
  
  }
  }
  

void onPulse()
{
  pulseCount++;
  //Serial.print("pulsecount=");
  //Serial.println(pulseCount);
  lastTime = pulseTime;
  pulseTime = micros();
  duration=pulseTime-lastTime;
  totalDuration+=duration;
  //Serial.println(totalDuration);
}

Sample output:

19.29 degrees C
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.14925
yawn ...
-- good morning!
19.29 degrees C
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.14916
yawn ...
-- good morning!
19.29 degrees C
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.14913
yawn ...
-- good morning!
19.61 degrees C
sampling period=2 sec; #pulses=14; duration per pulse (sec)=0.14924
yawn ...

And this is pretty good (is it a coincidence how close the values are?) given the theoretical prediction for the duration per pulse, using the astable 555 timer formula, and the resistor and capacitor values I'd used:

RA=21000;
RB=47;
C=10_10__-6;
frequency=1/(0.7_(RA+2_RB)_C);
1/f = duration per pulse = 0.14765799999999998