The microwave oven can help.
First of all, it is a complete myth and totally incorrect that microwave ovens "heat from the inside out." They do no such thing: the outside get hot first (do a roast and the inside will be pink and the outside will be done, just like always).
However ...
Most microwave ovens have a "defrost" feature that pulses the microwave energy on and off, and lets the heat being generated near the surface of the meat migrate inward before the surface gets hot enough to start cooking.
You probably already have the meat in the smoker, but if this happens again, put it in the microwave, using the defrost setting, for at least 20-30 minutes, while the smoker is coming up to temp. I think you will find that this will mostly solve the problem.
This microwave defrost technique is also useful if you are going to do a relatively low temperature smoke (i.e., you set the smoker temperature to something well below the common 225 degree F setting) and are worried about having the meat spend too much time in the "danger zone" of 40-140. By pre-heating using the defrost, you won't begin to actually cook the outside, but you can get the meat from the 35 degree temperature of the fridge to something closer to room temperature.
