Caching plugins and responsive design code in template files

I’m using some slightly hack-y responsive PHP code — using WP Mobile Detect to output one of two versions of a logo depending on the user’s device — but I’m also using W3 Total Cache, which I assume means if, say, a mobile user visits a page first, the mobile version of the logo gets cached and displayed to all users thereafter, no matter the device.

Assuming I need to use a caching plugin, can anyone suggest how I might still output the device-appropriate version of the logo? Is CSS’s “@media” declaration an option? I tried and failed, but it may be I’m just not facile enough with it yet.