This is one of those questions that has consumed historians pretty much since the Cold War began. This is a fierce historiographical debate on top of a complicated factual question, but I'll try and lay out the various positions.

Roosevelt is pretty famous for having been extremely controlling in his conduct of foreign policy; his own stated preference in overseeing the state department was to make sure that the left hand never knew what the right one was doing so that he would always be in supreme control. By 1944, many of his closest advisers such as Sumner Welles had been pushed out, which increasingly left him running the show even more. He's also frustratingly evasive even in the written record; FDR's response to memos might simply consist of a checkmark, from which we have to try and discern what he really wanted or how he stood on a given policy.

As you might know, Truman was a compromise pick for VP, and Roosevelt only met with him a handful of times before he died. Truman wants to try and sustain the foreign policy wishes of FDR, but doing so proves to be frustratingly difficult because he didn't actually have a concrete sense of what they were The people who were in ascendance around Roosevelt at that time such as Averell Harriman had been pushing for a hard-line against the Soviet Union, but Harriman had always ambivalent-at-best about the USSR.

Here's where it gets complicated, because to say how whether Truman bears responsibility for the Cold War, especially in this transition, rests on an extraordinarily sticky historiographical question that diplomatic historians are still debating to this day. The so-called "orthodox" historians who lay most of the blame on the Soviet Union for the Cold War naturally downplay this transition as a factor, and many suggest that Roosevelt was already pivoting away from the Soviet Union by 1944. John Lewis Gaddis (who is mostly on the orthodox side of this debate, especially later in life) in The Origins of the Cold War asserts that Roosevelt, who depended on Polish-Americans and Eastern European immigrants in his New Deal coalition was concerned about Soviet encroachment in Eastern Europe. Given that even the most generous interpretation of Stalin's behavior suggests he would only ever tolerate friendly, ideologically-aligned governments on his borders (if not Marxist puppet governments), Roosevelt would have grown more uncomfortable with Stalin given his behavior there and the domestic ramifications. Other historians make hay out of Roosevelt's increasingly infirm condition by 1945, pushing that his aides did too much of the negotiation at Yalta, leading to giveaways of territory that were unacceptable to many people, including Truman.

Then there are others like Frank Costigliola, whose book Roosevelt's Lost Alliances makes the case that the transition was at least a significant factor in the beginning of the Cold War. Costigliola argues that Roosevelt had brokered an accommodation with Stalin that simply assumed that the postwar world order would be formed out of spheres-of-influence, and that Stalin would frankly need an Eastern European zone after the twin traumas of the two world wars. He alleges that Roosevelt's advisers like Harriman failed to appreciate this, and to put it simplistically, had a number of hangups that led them to interpret Soviet behaviors in the worst possible way. Similarly, Truman's behavior was aggressive and direct in a way that Roosevelt's careful diplomacy never had been. So within just a few days of becoming president, Truman's berating the Soviet foreign minister about their failure to hold democratic elections in Poland. Truman openly says before Potsdam to an adviser that Stalin seems like the party bosses he knew in Missouri like Tom Pendergast, and that the best option was to be tough and direct with them. With somebody as hyperattuned to insult as Stalin, that was a poor combination.

Melvyn Leffler's A Preponderance of Power (or as we like to call it, A Preponderance of Pages) is a brilliant look at how U.S. foreign policy was informed in the postwar period by needing to match the Soviet Union, and he makes it pretty clear that Truman and others tended to see Soviet behavior in the worst possible light at any given moment. Some of that is this constant analogizing back to the Munich Compromise and the sense that that had been the opportunity to stop Hitler without all of the ensuing bloodshed, and so compromise or accommodation with Stalin now could lead to similar disaster.

So, this is in many ways an unsatisfying answer, but that's because we're still arguing about this in mostly congenial ways. Where do I stand personally as an academic? I'm more in the camp of Costigliola and Leffler, seeing American actors provoking Stalin at a moment when he was genuinely more interested in accommodation, however narrowly constructed it was (and it was, to be sure). Costigliola is particularly good at pointing out that we've always treated Soviet actors like they were irrational, and to be sure, they were. Stalin being irrational however doesn't make Truman, Churchill, or Harriman rational either, and you do see these repeated references in people's papers to Munich and connected lessons to appeasement and compromise. Those Munich analogies never really go away (I vividly remember them being made about the Second Iraq War), but they're very strong in this period because they emotionally resonate with people. Unfortunately, they're also very problematic because Hitler and Stalin were strikingly different people, down to ambitions and how to carry them out. Costigliola makes the case that yes, Stalin saw competition as inevitable with the capitalist bloc, but not necessarily violent or immediate. Stalin was cautious and fearful of his own weakness, while Hitler was all aggression and risk. That doesn't absolve Stalin of anything, but a narrative that holds him as solely responsible doesn't capture the full complexity of this, and some of that complexity should come back to Truman.

But those are other questions, and I don't want to bog you down in other issues. Hopefully some of this was enlightening.