Hi there! What a lovely home - we would agree with bigreader, rugs would definitely help soften those hard surfaces and can add another element of colour to tie the room together - one under the dining table, or one in front of the lounge, or both!

If you're trying to avoid adding warmth, try to avoid rugs that have a deep pile and opt for low pile woven or tufted options. Another thing to consider is the materials of the rug - soft fibres like bamboo and silk are cool to the touch as opposed to materials like hemp which have a "warmer" feel underfoot.

In terms of colour, I noticed you have accents of green in your chair upholstery and artwork - try to keep to cool greens or blue/greens to offset the warm wood tones.

A few suggestions:

https://www.designerrugs.com.au/rug-collections/designer-collaborations/catherine-martin/black-pearl/

https://www.designerrugs.com.au/rug-collections/designer-collaborations/hare-and-klein/etched/

https://www.designerrugs.com.au/rug-collections/designer-collaborations/catherine-martin/night-bird/

https://www.designerrugs.com.au/rug-collections/designer-collaborations/catherine-martin/rhapsody/

https://www.designerrugs.com.au/rug-collections/designer-collaborations/hare-and-klein/shadows/

https://www.designerrugs.com.au/rug-collections/designer-collaborations/house-of-heras/waratah-wonderland/

https://www.designerrugs.com.au/rug-collections/handknot-collections/contemporary-hand-knot/glory-days/

https://www.designerrugs.com.au/rug-collections/handknot-collections/classic-handknots/fleur-ivory-blue/

https://www.designerrugs.com.au/rug-collections/handknot-collections/classic-handknots/fleur-green/

https://www.designerrugs.com.au/rug-collections/handknot-collections/mystique/majesty/

Hi there! So sorry for the late reply! They don't necessarily need to match, but keeping the style similar would be a good idea - art deco paired with art deco, contemporary with contemporary. If you do go with a matching design, you can always customise the colours or even the scale / placement of the design so that you have rugs that complement eachother but are not exactly the same.