Mild-mannered and slightly stiff in bearing and walk, you sense a very different style of leader from his predecessor.
Years of daily work-outs and strenuous judo bouts, plus eight years of being Russia's top man had given Vladimir Putin - a leader presiding over an economic and security renaissance - the cocky swagger of a victorious sportsman.
Mr Medvedev's self-confidence is more composed.
His English comprehension is good - he clearly didn't need the interpreter who translated my questions for him.
He gazed inscrutably as he composed his responses and answered calmly and methodically, betraying his lawyer's training.
No impassioned rhetorical flourishes, embellished with earthy language, as Mr Putin was prone to.
It is hard to imagine Mr Medvedev letting loose with such colourful language that the Russian translators would feel obliged to edit out choice phrases.
In the end, though, it was hard to gauge whether he wanted to reassure the West or increase its sense of foreboding.
The recognition of South Ossetia and Abkhazia, he said, had been forced on Russia because the violence at the beginning of August had changed everything.
He blamed what he called the Georgian regime's attempted "genocide" of innocent Ossetians (never mind that the officially-declared death toll has dropped from thousands to a few hundred), which he claimed meant Georgia ought to forfeit its right to control the territory.
He denied that declaring the two enclaves independent in any way breached the spirit of the ceasefire document he had signed with French President Nicolas Sarkozy (which had identified as its sixth step international discussion on their future security and stability).
And he insisted that the presence of Russian troops deep inside Georgia's territory, including around the port of Poti - nowhere near any buffer zone - was also allowed under the terms of the ceasefire.
This was the only way, he claimed, that Russia could fulfil its peacekeeping role of guaranteeing security, to make sure that Georgia could not re-arm and start fighting again.
"Our aim is to suffocate aggression," he said.
What came over was not reassurance, but a warning that Russia will not be deflected from its aim, and that other nations in the region should watch out before invoking Russia's wrath, as it had the power and the political will to take action.
Asked why Russia was acting so unilaterally, Mr Medvedev said that of course Russia would protect its own interests, especially when they coincided with the security of Russian citizens.
I asked him whether, if it was his duty to protect Russian citizens, other republics with sizeable Russian-speaking populations like Ukraine, Moldova or the Baltic states could possibly expect similar treatment.
Many South Ossetians feel closer to Russia than Georgia
He would only say that Russia had the right to self defence, and he as president had to guarantee the safety of Russian citizens.
Asked if he thought there could be another Cold War, he answered that Russia did not want a return to a confrontation in which no-one would be the winner.
He wanted pragmatic productive relations with Western partners based on mutual respect, he said.
"We don't want any Cold War... Whatever some statesmen say there are no winners in a Cold War - that's why we don't want any confrontation or any tensions," he told me.
But he did not rule out the Cold War option, or suggest any way to reduce the current mounting tensions.
It was hard not to conclude that although the Russian leadership is concerned at the lack of clear support for its actions internationally, it is also revelling in its newly-found fearsome image.
Others may talk about the appeal of soft power and getting people to want to join you of their own accord.
But the hard power of flexing military muscles in Georgia has suited Russia just fine, it seems.
If the world is intimidated and dismayed, so much the better, Mr Medvedev appears to be suggesting.
This is a country, it seems, that is in no mood to bow to diplomatic pressure from the US and Europe, even if at the same time it wants to retain some semblance that it is business-as-usual diplomatically, in order to continue to prosper and enjoy its own stability.
No wonder Mr Medvedev's fellow G8 leaders found him so difficult to read at their July summit in Japan - is he a partner or an opponent?
One of my final questions was to ask: who really runs Russia? Mr Medvedev sat up tall and a note of self-importance entered his voice.
"If any country allowed its military decisions to be taken by committee it would be disastrous," he said.
"And if you want to know who gave the order, let me tell you, there is only one commander-in-chief in Russia."
He was expecting the question. He enjoyed the answer.
But I was left with the impression that somewhere Mr Medvedev was going through the motions - he didn't really believe he is yet Number One in Russia.
And it seemed that behind the scenes, Vladimir Putin, even if he has taken a backseat role on Georgia in recent days, nonetheless keeps his hand on the tiller.
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