Okay so there are a few concepts mixed up here so I will answer as best I can. Firstly, you are correct that gas has a pressure that increases with heat, however pressure is a large-scale concept that only exists when considering hundreds of thousands of particles. When discussing two individual atoms, it doesn’t make sense to discuss pressure.
Next is the idea of repulsion. In order for two particles to repel one another, there must be a force between them for example an electrical force or a collision. You were asking about atoms, which are charge-neutral particles and therefore have no electrical or magnetic forces between them. You talked about repelling at different distances which I’m assuming means that your atoms are separated and therefore not colliding. This means that there are no forces between the atoms so they would not repel one another at all. If, however we were discussing charged particles that had an electrical force between them, then the answer to your question is that temperature has no effect on the strength of the repulsion.
You are mixing up scales. Sure higher heat = higher pressure but thats only for groups of molecules, very very large groups.
Hot or cold for individual atoms just means how fast they are moving, how much kinetic energy they have. It won’t impact how they repel/or attract other atoms, it just increases the frequency at which they collide (and the energy at which they do so, usually making them more likely to react).
Think of them like bumper cars (assuming no reaction). Faster cars means bigger bump, but the distance at which it bumps is the same.
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