>Many times I have been to barbeques where things have not been properly cooked through to the centre either because the barbeque hasn't got to the correct temperature . . . .

More often the opposite I think. The temperature is too high so the outside starts to burn before the middle has time to cook.<

Oh yes I agree the charcoal should be white hot before you start to cook rather than flames so that it cooks properly but my over-enthusiatic ex-hubby would try to start cooking it far too soon and the result would be a chard outer bit and a pink middle. (Even scarier when he came up with the idea to use lighter fuel). That was one of the reasons to start things off in the microwave, just in case!