You say you are using this machine with the battery removed. I wonder if that is part of the problem, in that the mains power unit supplies a (slightly) higher voltage, in order to charge the battery. Without the battery to absorb this, the internal power unit is having to deal with it, and this could well lead to overheating in the circumstances you describe.
It might be worth replacing the battery, and see if the fault recurs.
be wary of strong drink - it may make you shoot at tax collectors, and miss!