Siberia is already very hot in the summers. Like 40C+ in the summers and -40-50C in the winter. That range is not going to be 'Mediterranean' anytime ever.
Siberia is vast, checking one town for it's climate is not representative. While most of the southern part of Siberia is relatively mild (like nothern central US) there are huge regions that are known for more extreme temperatures, in particular Sakha (Yakutiya): https://en.wikipedia.org/wiki/Sakha#Climate
The context of the point is that Climate change's max increase is only another 0.5celcius and at worst the currently too cold places will become warm enough to live comfortably.
How many people are going to live there? Supported by what infrastructure? How is the infrastructure going to be maintained? Where are all the machines that you need to repair and replace the infrastructure? Where are the plants to produce the machines? Who is going to maintain the infrastructure, the machines and the plants? How do you decide who's going to get to Antarctica? How are you going to prevent other from going there themselves? How are you going to stop the rest of the world from nuking Antartica in retaliation? How are you going to stop the USA and China from going to war over that last habitable piece of earth? How are you going to provide food and oxygen to the few survivors?