Hello, this is my first post, so im a little newbie, anyhow, im trying to make an incubator, the major goal its to mantain the temperature around 35-37C, to do so i have an arduino mega, an LM35 temperature sensor, a peltier plate, and an LCD 16x2. I need help to connect everything together and writing the Code. If everyone can help us i would be greatful.
If you guys want more information, the goal its to make a shaker within the incubator, the shaker its already done. But im having heavy troubles with the incubator. Thanks!
What you need to do is draw a block diagram of how you expect things to all fit together. Then you need to define just what you want to have happen as far as how tight the temperature control is, are you going to have something to circulate the air in there so you don't get hot spots? One thing to be very careful of is to make sure your heat source does not heat the system up so fast that the control loop (Arduino, temp sensor, power control) does not get a chance to respond properly. That leads to creating an oscillator 
Once you have done that, then you identify tasks in your code and block it out. People here will help you work with the code and help find problems, but they are not going to write it for you. You need to spend some time figuring out (lots of examples including in the IDE examples directory) how to control/display on the LCD etc. Figure out what your power requirements are - that peltier plate may be a power hog.
You can read this site for more info
LM35 Incubator with LCD 16x2 on Arduino
You also need to know the thermal isolation of the container thats being used.
ie whats the rate of heat loss for the coldest external ambient temperature.