Be careful as high accuracy will come with a high price tag, what are you making that needs to be manufactured to that degree of accuracy???

Not so sure about your cooling/heating idea for the aluminium frame, aluminium will expand at twice the amount of steel but for a machine as small as you are describing then not so sure it would be necessary.

For instance, a 100mm length of steel will increase or decrease in length by 0.00126mm for every degree C of temperature change so a temperature change of say 20 degrees C will change the length by 0.0252mm, aluminium will be approx twice this with a change of 0.048mm.

Buy yourself a good heater for the winter and open the doors in the summer then you should not see much difference!