Can a nuclear power plant have an effect on the weather?

Answer 1

In the strictest possible sense, yes, since it does release heat into the environment. However, it will have MUCH LESS of an effect than a fossil fuel power plant, since there are no combustion gases involved.

Answer 2

The reactor makes heat (a lot of it!) which heats up water called Primary Coolant. The reactor and the primary coolant are sealed inside a containment building to prevent the spread of radioactive particulates in case there's a leak.

Depending on the design, there may be a secondary water system that is not radioactive and is boiled off using the heat from the Primary Coolant, making steam. This steam pushes on a turbine attached to an electric generator to make power. Once the steam is done, it is condensed back into water using an external cooling source (usually water from the ocean or lake or river)

The large distinctive towers that you see in a nuclear power plant are the cooling towers where massive amounts of water are boiled off as a heat sink. There is no radioactive release anywhere in this process, it is all contained inside the sealed containment building.

So, what effects does it have? Well, there's heat pollution, caused by the release of (non-radioactive) steam in the cooling towers. There's also the issue of what to do with the spent fuel once it's used up. Currently the fuel is sealed up in special containers and are buried in remote locations.