The only part of the cylinder in vacuum is the portion outside the penis - space between the shaft and walls of the cylinder if any. If you use a water based lubricant it will dry off very quickly when exposed to full vacuum.
I start with a water base to moisturise the skin then change to petroleum jelly because it does not boil off under the vacuum.
When the vacuum is pulled the pressure within your body remains at atmospheric pressure. The pressure can reach a maximum of 14.7psi at sea level. Under full vacuum that is the pressure applied to the inside of the penis until the shaft is hard against the side of the cylinder and the head is against the end of the cylinder. If the shaft is not against the cylinder then there is large hoop stress on the shaft increasing the girth. Likewise if the head is not against the end there is high stress on the glans and the ligament.
There is no particularly magic about a pressure of 14.7psi. It is less than three times 5psi. I can stop water flow in a 1/2” hose with my thumb. With the water pressure at 50psi. My thumb does not explode. Standing on the heal of one foot I expose that portion in contact with the floor to about 40psi. On the other hand I would not put a vacuum cleaner nozzle near my eyeball or ear drum because even that level of pressure below atmospheric (about 3psi) could do a lot of damage to those sensitive organs.
Most industrial air compressors operate at 90psi. If that pressure gets under the skin in some way it can do tremendous damage to tissue. Putting an air hose in your mouth and opening the valve will cause you to explode.
Heating of the penis would indicate increased blood circulation. Under full vacuum the circulation is very poor and the tissue cools down. Cycling the pressure - say 5 seconds to full vacuum and release to almost no vacuum over about 2 seconds - increases the blood circulation due to the expansion and contraction of the tissue and this will cause the shaft temperature to rise.
When I refer to full vacuum it is in excess of 14psi. Completely evacuating a gas chamber requires a long time and good pump. So in terms of vacuum there is a large difference in the amount of effort to extract the very last molecules of air to get from 14psi to 14.7psi but in terms of the stretch it is only 5% difference. 95% of the stress is achieved at 14psi, which is easily achieved with a single stage industrial pump.