The Cold War is a long period and you didn't specify which countries you meant. But let's imagine you wanted to know about US/Soviet cooperation during, say, the post-Stalin era.

In many fields there was open publication and no export control, so there was in effective informal cooperation. So the US read Soviet journals and vice versa. In fact some of the earliest work on machine translation was done to help automate the translation of Soviet technical journals into English so that American researchers could benefit from them. There were also, in the post-Stalin era, international conferences where Soviets and Americans were allowed to attend and talk about open topics.

In some fields, there were export-controlled or classified results, even for things that didn't have explicitly military value. So high electronics is one of those areas. Microchip processors were highly export-controlled in the West and while the Soviets could (sometimes through intermediaries like the Stasis) acquire specimens, they had a hard time acquiring them in bulk and an even harder time reproducing them (since importing a microchip foundry is a lot harder than importing a chip). The list of technologies under export control agreements in the US is very long and contains a lot of pretty innocuous-looking stuff.

In general though, to my knowledge there wasn't a lot of direct cooperation, e.g. being partners on a project, or the Soviets importing US expertise or vice versa. There is some of that very early on the Soviet regime (the Soviets brought in American engineers to help with the Dnieper dam, for example), but I don't know of any post-WWII examples of something like this happening.

There were a few high-profile direct collaborations, like the Apollo–Soyuz project, but these were unusual. The more common model was, "let's set up some kind of international body or record of work or a journal or an archive, and we'll each make contributions to it, and we might get together and talk about the results, but we're still mostly doing our own thing, albeit with knowledge of how you and everyone else who is willing to participate is doing it."

In terms of countries outside of the US/Soviet orbits, the more common model was one of competition, e.g. like the Aswan dam.