Need guidance with themosistor and relay

I don't have any problem with the LM335. I'm doing a double reading of pin 0 and 1 every 10 sec and I always have a constant reading. 1 sensor is off by .6 degre but if I switch the order of the sensor, I ended up with the same reading. Here is my sketch for the temperature reading:

if (millis() - previousMillis > interval){
for(int i = 0;i<=1;i++){ // read twice as the 2nd reading is more accurate
temp_out = CheckTemp(0); // Outside thermometer is on pin 0
temp_in = CheckTemp(1); // Inside thermometer is on pin 1
if (temp_out > temp_in){
digitalWrite(motorPin, HIGH);
}
else{
digitalWrite(motorPin, LOW);
}
}
previousMillis = millis();
}

Second,
what you said makes a lot of sence and I would never have thought about it by myself. I was using a relay because... my level of knowledge is still pretty limited.

Could you give me a transistor reference number so I can find something equivalent. I almost understand what to look for when looking a a P2N2222A reference sheet (Motorola 2N222 datasheet pdf) but I'm quite lost when looking at a mosfet sheet (HTTP 301 This page has been moved). The terminology is not the same (collector, base, emitter VS gate, drain, source).

Thanks