The full picture is more complicated. Whether switching from fossil/nuclear to wind would change patterns of energy service demand, and energy efficiency, is an open question, so there are plenty of ripple effects. But, putting those aside to simplify things, just switching from fossil/nuclear to wind wouldn't create new sinks for the low-grade heat: lighting would carry on getting used at the same time and place as it does at the moment. What would happen is that energy would be extracted from the wind in new places: at turbines, rather than further downwind where the energy would be dissipated by friction. The other thing that would change is that there would no longer be additional sources of low-grade heat at all those fossil and nuclear power stations. Now, they're pretty intense sources of heat: nuclear or coal plants typically push out 150% - 200% as much energy as local heat, as they do electricity. So that's a signicantsignificant input of heat into a local weather system, which would no longer be there when they're turned off because the electricity is being supplied from wind instead.
On top of what I've written above, we've also got a bunch of modelling in the literature. Now, this is largely a bunfightan argument between different assumptions: pick the answer you want, and tune your assumptions accordingly. However, these papers are written by people with different axes to grindunderlying positions, so you'll find a range of possible outcomes, and you can decide for yourself which assumptions are more or less likely.
Wang & Prinn looked at potential long-term global impacts of multi-terawatt-scale installations and found that massive onshore wind turbines might cause some warming over land (though less than the coal & gas plants they would replace), and massive onshoreoffshore wind turbines might cause some global cooling. The modelling was done by assuming the turbine interactions would behave like a generic increase in surface roughness; the other key assumption is that the loss of detail from meso-scale modelling did not significantly impact the results.