The coupled electron–ion heating equations, neglecting losses, in a CO2 laser heated solenoid are solved for a laser intensity varying with time as I = I0t2/3. An analytical solution, without restriction on the ratio of electron-to-ion temperatures Te/Ti is found, showing Te,i ~ t2/3.The heating wave which propagates along the solenoid is found to be supersonic having a velocity independent of time and varying as I03/5. Low intensity heating is found to maximize Ti/Te and minimize plasma length and laser energy requirements. The heating wave propagation is found to be consistent with an optical thickness of order unity in the heated plasma column. Considerations of electron–ion energy transfer, supersonic heating wave propagation, and laser beam trapping lead to an optimum laser intensity parameter [Formula: see text].