Jesus actually got this wrong. It was not in fact written that thou shalt not tempt the Lord thy God.

I think you are making an elementary error: from "the Bible says not-X", inferring "the Bible doesn't say X".

Deuteronomy 6:16 says "You shall not put YHWH your god to the test as you did at Massah". That's a reference to the events described in Exodus 17:7: "[Moses] named the place Massah and Meribah, because the children of Israel quarrelled and tested YHWH, saying 'Is YHWH among us or not?'." That's the bit where they get all grumpy at Moses because they have nothing to drink, and he strikes a rock with his staff and produces water.

So it's all a bit flaky, but I don't think Jesus is wrong here. The Israelites get grumpy and accuse Moses of bringing them all this way out into the desert to let them die of thirst; Moses performs a miracle to give them some water and reassure them; God, as purportedly quoted by the author of Deuteronomy, interprets this as putting God to the test (this, if anything, is the dubious bit; the story in Exodus sounds as if their problem was thirst more than it was doubt) and tells them not to do it again; Jesus appeals to this when challenged to demonstrate that he, like Moses, has God on his side. (Digression: It seems to me that his response here would have been better as a response to the previous temptation -- to make rocks into food -- which is awfully reminiscent of what the Israelites had had Moses do. I wonder, and this is pure baseless speculation, whether at one point there were two temptation narratives going around, both involving the stones-into-food challenge, with Jesus giving the "man does not live by bread alone" answer in one version and the "do not put God to the test" answer in the other -- and then Mark or Q or whoever wanted to include both stories but needed a second temptation, and therefore made one up. This would also explain why the second temptation is such a silly one.)