Do you know if there is some reason the built in heater does not bring the tube to 'full operating temp?' I ask this because it looks like just upping the thermostat to 45C would have the same effect as keeping the lamp on all the time.
The heater should turn off when the lamp turns on. The heater thermostat needs to be set at the steady-state lamp-on-forever temperature. Aristo has (hopefully) calibrated the thermostat so that it turns off as the lamp turns on. There may be a relay that turns down the heater when the lamp is turned on to assist in this action.
Covering the vent holes has probably upset this relationship. I would suggest uncovering the holes. Changing the thermostat setpoint will most likely not help matters as Aristo has (again, hopefully) made the system work acceptably as originally designed.
A thermocouple attached to the lamp will give you an indication if the system now holds the lamp temperature somewhat constant. Radio Shack sells cheap digital volt meters that come with thermocouple probes. Obviously, if the light output is steady from turn-on then the heater is doing its job and you don't really need to measure the temperature.
If uncovering the holes fixes the warm-up problem then an external light baffle is the solution to lessening the stray light.
I am not familiar with this enlarger or this Aristo light source, but Aristo grid lamps are sometimes designed to mount inside of or as a part of the existing original enlarger head. Aristo may have been using some part of the original lamp housing to baffle the light from the vents.
An email to Aristo may help clarify matters.