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Unfortunately it is not possible to make specific recommendations for thermoelectric cooling systems based on temperatures alone–the power dissipation of your spectrometer and the details of the mechanical system design will have very significant effects.
The resources below discuss the application of thermoelectric systems and thermal modeling in some depth. In my experience, the great majority of those who attempt to use these devices without taking the time to understand the theory and do the math will fail in their efforts, due to the absolutely brutal inefficiency of currently-available devices.
The DA-011-05-02-00-00 device mentioned is a nice example of the sort of product that is available, but will not work in your application. Achieving a net cooling effect of 55°C for a device that dissipates a significant amount of power is not trivial, and may approach the limits of what is possible with a single-stage system. As a rough estimate, I’d expect that a thermoelectric cooling system would consume about 50x the amount of power being supplied to the spectrometer under the conditions mentioned.