Texture is one of the three colour elements of designing a scheme (colour and light being the other two). And there are two points to make.
A navy blue velvet sofa will have a very different feel to a navy blue linen sofa. The former will feel distinctly warmer than the latter, despite both being a cool blue tone. This means that you can devise a scheme with different degrees of warmth even using your favourite cooler colours. And it works the other way around too. If you’re concerned about having too many warm tones, use lightweight, understated textures, like finer linens and light-reflective, glossier finishes over matte ones.
Colour aside, the mere presence of different textures in a room will always turn up the temperature purely on the basis of there being more things to touch and feel – the fuzz of a sheepskin rug, the drape of a chunky throw, the gleam from a glass vase or lamp.