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Water underfloor heating and hugs

I'm planning a large open plan living area and because we are installing water underfloor heating I need to put tiles as the flooring finish so we can feel the heat optimally.
I would like to also use rugs to help zone for instance the sofa/TV area and under the island to break up the cold kitchen feel. Also with such a large space the rugs will make it feel more homey
Will I still feel the heat if I use rugs?
Do people opt for thinner rugs to avoid any heat loss?
How do people use decorative rugs when they have underfloor heating?
Thank you 🙏😊