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3/0 or250 aluminum
THHN wire is moisture resistant thermoplastic allowed for use in dry and wet locations. Maximum temperature is 60 C or 140 F. Being thermoplastic it should not be handled below 0 C as cracking of the insulation could easily occur.
The short answer, if using copper, is 0 AWG, commonly referred to as 1/0 or "one ought". Type of wire depends on location & temperature, but in my common scenario I am using 1/0 THHN inside a 2" schedule 40 PVC conduit (3 - 1/0 wires plus a 4 ga bare ground) to run indoors, a distance of about 25 feet from my main panel to a sub for upstairs. I could go into more detail regarding outdoor, direct burial, grounding, aluminum wire, etc but would need more details.
WIRE AMPACITY TABLE ACSR DIA.(OUt) CCC 795MCM 1.093" 900 A 556.5MCM 0.927" 730 A 336.4MCM 0.721" 530 A 4/0 0.563" 340 A 3/0 0.502" 300 A 2/0 0.447" 270 A 1/0 0.398" 230 A 2 0.316" 180 A 4 0.250" 140 A 6 0.198" 100 A
According to the 2008 National Electrical Code, the smallest wire that can be run in parallel is a 1/0 AWG (American Wire Gauge). If the wire you are using is smaller than a 1/0 AWG, you will need to increase the size of the wire to handle the amperage (Table 310.16 of the NEC).