Sorry Ira, I can't help you there. You're probably better off using a ac adapter and powering the DC in jack instead which is probably better and more efficient than using the converter. The reason is that the converter is going to be a transformer which in turn is going to power another transformer (inside the boombox). Due to the inefficiencies of the power conversion, doing it twice is probably the least desirable way to do it. The heat you are feeling is the waste energy produced due to the inefficiencies of the converter and probably the high guage wiring which has too much resistance.
Another thing you might want to look into is the existing transformer in your boombox. Many transformers have more than 1 set of coils which allows the transformer to operate on multiple input voltages. If your existing transformer has an unused center tap, powering the transformer from that lead will most likely result in the proper output voltage on 110v input. This is a rather simple change that will have no external signs of conversion.
In fact, my Japanese RX-7700 is 100volts only. I also have a US version with multivoltage selector. Both use the exact same transformer. The only difference is how the transformer is hooked up and which leads are used on the inputs. Needless to say, changing it over to the correct voltage was no issue at all.