Is this a dwelling unit? 220.82 only applies to dwelling units, and for service load calculations, and not related to tap conductors. Information you provided indicated not a dwelling unit.
Are you trying to justify the smaller conductors, already installed?
Are you providing just one set of conductors for both loads?
Additional info related to heating loads:
220.51 Fixed Electric Space Heating.
Fixed electric space-heating loads shall be calculated at 100 percent of the total connected load. However, in no case shall a feeder or service load current rating be less than the rating of the largest branch circuit supplied.
Exception: Where reduced loading of the conductors results from units operating on duty-cycle, intermittently, or from all units not operating at the same time, the authority having jurisdiction may grant permission for feeder and service conductors to have an ampacity less than 100 percent, provided the conductors have an ampacity for the load so determined.
AHJ may allow for undersized conductors with justification. Seems some arbitrary criteria involved. Would think it would require some equipment that would prevent simultaneous operation.
Also:
670.4 Supply Conductors and Overcurrent Protection.
(A) Size.
The size of the supply conductor shall be such as to have an ampacity not less than 125 percent of the full-load current rating of all resistance heating loads plus 125 percent of the full-load current rating of the highest rated motor plus the sum of the full-load current ratings of all other connected motors and apparatus, based on their duty cycle, that may be in operation at the same time.
Informational Note No. 1: See Table 310.16 through Table 310.20 for ampacity of conductors rated 2000 volts and below.
Informational Note No. 2: See 430.22(E) and 430.26 for duty cycle requirements.
No indicator as to type of industrial heat being provided.