For this to be done its not all that big a problem, I incubate reptile eggs which sometimes have a tolerance of about 1C either way, I have made my own thermostat do exacly what i want it to as the ones on the shelf are pants. The thermostat i have is Pulse Proportional, it has a setpoint and then the heaters job is to match the setpoint, as the temperature increases the heater will begin to turn on and off it is done in a series of pulses, sets of 5 for 1 second per pulse, (eg: off,on,on,on,on) as the temperature gets closer to the setpoint the off pulses get longer (eg: off,off,off,on,on) this pattern just fluctuates nicely when it reaches a sort of happy medium. This takes care of overshoot and hysterisis is minimal.
Doing this is easier than using phase angle, and better accuracy than relay operated thermostats.
Humidity can also be factored in the same way as heaters, all i do is set it to mist the enclosure every 5 mins depending on the actual RH, due to the nature of RH it takes a while for reading to emerge, i.e spraying the tank doesnt give instant results, it takes a few minutes to get an accurate readout.
If your incubator is a pro egg hatching type it may already have a egg turning mechanism built in, iff not this can be acheived quite easily also.