Chiller advice: External probe / External thermosta - Any difference?

[Emokidz]

Title should read: Thermostat*

Hi guys, I'm just wondering, is there any difference between connecting an external sensory probe to the chiller (placing it in the tank, in place of the original probe which measures temperature of the chiller's internal reservoir) and an external thermostat (external probe connected to chiller's power supply and controls power supply to the chiller based on a temperature range I can set).

In the former, the power is always available to the chiller and it kicks in and out depending on whether the temperature in the tank exceeds the temperature set on the chiller. Hence the chiller kicks in and out as and when it needs.

In the latter, power is only supplied to the chiller once temperature goes out of the range set on the external device which measures tank temperature. This means that the chiller kicks in everytime it is turned on. What I'm worried about though, is that the external thermostat cuts power supply once the desired temperature is reached and the chiller shuts down abruptly and isn't able to complete the kick out duration. Are there any consequences to this?

[Shadow]

Cost different, temperature controller is much more expensive. I'm not sure the impact of sudden power cut off to the chiller. Also if you notice, chiller have few seconds to minutes after power ON before it start the actual cooling, even when water temp way above set temp.