"Mic" as an abbreviation for microwave
Solution 1:
Searching for "heat it in the mic" (in quotes) on Google comes up with a number of results, most of them of the forum/blog variety. I think this is evidence enough to show that mic is in use as an abbreviation for microwave, particularly (as you'd expect) in casual contexts.
As I've never heard it used before and have lived in many different US states, I'm inclined to say it's quite dialectical. Which dialect, though, I'm not sure.
Solution 2:
I've never heard of "mic" as a shortened form of "microwave". I have seen it used for "microphone" many times, particularly on audio equipment, where space is at a premium.
Interestingly, there's a disagreement in the audio community (at least in the US east coast area) about whether we should talk about an "open mic" or an "open mike". "Mic" sounds like "mick" when you say it, but you refer to a "mike-ro-phone", not a "mick-ro-phone". There's an argument that "mic" violates English spelling rules, but this is somewhat specious since we're talking about a language where every rule has exceptions - often many of them. (For more information on why "mic" is incorrect, have a look at this entertaining tirade.)
Merriam-Webster lists "mic" as short for microphone, Micah, or methyl isocyanate. The Online Etymology Dictionary lists it as a shortened form of microphone. Cambridge US and British concur. Pulling out the big gun: The Oxford English Dictionary lists, under "mic", the meaning of "microphone". The definition for "microwave" doesn't mention any abbreviations (but the definition for "microphone" also doesn't list any.)
Going by a descriptivist view, "open mic" gets 53,200,000 hits on Google, "open mike" returns 2,370,000.
In short, I'd conclude that "mic" as a shortened form of "microwave" is probably a regional variation and is not a common usage.
Solution 3:
I have heard it called a 'mic' by cooks and chefs.