S3 xenon headlight turning off when hot?

guinness

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The headlight warning light came on while driving tonight. Found the right dipped headlight off and thought it must be the headlight bulb that needs replacing.

But after parking it and coming back to the car, the bulb worked again - only to go off (and the headlight warning light came on) after a few minutes. Is this typical of a 'gas discharge bulb' on its way out?

I guess my first course of action should be to get the bulb replaced? Is a D2S 35W 4300K what I should be looking for?