Heat conduction between the armature and stator/casing of a metal cased electric motor is usually quite good . The metal construction, very small air gap and constant air movement all contribute very effectively to heat transfer .
With metal cased motors cooling the casing certainly helps cool the armature – simple heat sink effect . This is why many motors have ribbed casings and why some specialist motors have casings with proper designed in heat sinks using large area fins .
Heat transfer is mostly by simple conduction . Thermal Inertia effect is very small – time constant can't exceed 90 seconds and settling times must be of order of a few minutes at most .
Wound armatures do sometimes fail by bulk heating of the whole thing causing insulation failure and then shorting out but a far larger number of failures are caused by local defects in the windings . Most common of these local defect failures occurs when a length of the winding wire is in poor thermal contact with the rest of the windings . This separted length doesn't lose heat as well as the rest and runs hotter . With modest current flow this doesn't usually matter but with higher current flows ( and especially when motor is being run above its rated power ) the separated length gets very hot and fuses .
Using randomly chosen motors for dead slow plus high torque applications is always likely to cause heating problems . At dead slow speeds current drawn by DC motors is only limited by the winding resistances .
Properly designed electronics can improve matters a little but not really very much if motor is completely wrong for the application .
Older type permanent magnet motors ran hotter the older they became . This was due to gradual loss of field strength caused by magnets getting weaker with time . Modern magnetic materials are much better .Weak magnets were the primary reasons why early Hornby and Triang OO motors failed so often – magnets became weaker , current went up and sooner or later burn out happened .
When I worked at Mtu I often went over into Switzerland and that was a wonderful place to see electric motors . Many on the cable lifts and railway engines were 1930 to 1950 vintage and semi open frame with everything visible and beautifully constructed and maintained .
Michael Williams .