Were there positive steps towards a reduction of tension and thus a "thaw" in the Cold War after 1953?
Although Stalin died in 1953, things did not really get any better between the US and the USSR. I would say that there was not any such steps or any thaw.
It is true that the Korean War ended soon after Stalin's death in 1953, but this was not symptomatic of any lasting thaw. This was partly because of domestic politics in the US. This was during the McCarthy Era and no one in the government wanted to look like they were being "soft" on communism by proposing any real compromises. By early 1954, in fact, the US was willing to go so far as to announce a new doctrine in which it promised to use massive nuclear force to retaliate against any communist aggression anywhere in the world. This does not sound like a thaw in any real sense.