Check out the Fluke 116. It's got a thermocouple (type K) input, plus a µA range for doing flame sensors, plus all the usual mod-cons for volts/ohms/diodes etc... No current ranges besides DC µA though. If you need to measure AC current, I'm sure you could pick up a basic clip-on current transformer quite cheaply that'd do AC current at least as well as cheap tong.
If you can hang the expense, grab an 87V, or a Yokogawa TY530. Maybe check out Agilent too? I'm not so familiar with their range.