I based this on the version you gave in the very first post:
#include <math.h>
const int transistorPin = 9;
int tempPin = 0;
int tempReading;
int x;
float angle = 0;
void setup()
{
pinMode(9, OUTPUT);
Serial.begin(9600);
}
void loop()
{
tempReading=analogRead(tempPin);//temperature reading
x=map(tempReading,150,170,1,5);//map the reading to change the frequency
Serial.println(x);
angle += 20.0/1500.0*x*PI;
float val = (exp(sin(angle)) - 0.36787944)*108.0;//the function of breathing led
Serial.println(val);
analogWrite(transistorPin, val);
delay(20);
}