All electrical items carrying current get hot. The amount of heat is actually proportional to the square of the current, so doubling the current causes four times the heat.
A high current motor and controller can carry a lot of current - so can generate a lot of heat!
Motors - at least the ventilated ones - have a built in fan for cooling. Controllers do not. So a motor can generally be used at higher currents for longer than a controller since the heat will build up in the controller while the motor cools itself.
Fortunately most controller applications are land based and very ´peaky´: a machine on land generally only takes a lot of current to get up to speed or to climb a hill, both are usually only a few seconds.
This peaky heat generation is well suited to MOSFET technology and all controllers therefore tend to be rated for peaky use. To make a controller for continuous use, you either need to use a lot more power devices - i.e. use a bigger controller - or take steps to remove the heat quicker. Boats and other water craft need a continuous rating since the faster you go, the more the current: it takes power simply to move through water, not just to get up to speed.
The moral is: use a controller that will give a top current output perhaps 3-4 times the continuous motor current and do not expect a controller to run continuously at more than 25-30% of its short term rating.
The subject can get quite technical but a lot of information is given in our answers to all your questions on battery motor control pages.
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