If the wire is rated as THHN/THWN then that is what you would use for sizing the raceway. It should not have thicker insulation than any other THHN/THWN of the same size. The MTW is just an additional listing for the wire to be used for internal wiring of equipment. All of the small THHN/THWN I buy is also marked MTW.
Edited to add the Southwire info below:
Southwire SIMpull THHN or THWN-2 conductors are primarily used in conduit and cable trays for services, feeders, and
branch circuits in commercial or industrial applications as specified in the National Electrical Code. Voltage for all applications
is 600 volts. SIMpull THHN conductors are designed to be used without application of pulling lubricant. Allowable
temperatures are as follows:
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THHN or T90 Nylon- Dry locations not to exceed 90? C
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THWN-2- Wet or dry locations not to exceed 90? C or locations not to exceed 75? C when exposed to oil
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TWN75- Wet locations not to exceed 75? C
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MTW- Wet locations or when exposed to oil at temperatures not to exceed 60? C or dry locations not to exceed 90? C
(with ampacity limited to that for 75? C conductor temperature per NFPA 79)
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AWM- Dry locations not to exceed 105? C when rated and used as appliance wiring material
