Anything is serviceable if you have the knowledge, tools, and parts to repair it. It's entirely possible that the wheel could be the issue, however have you checked to make sure heater core isn't hot and that the A/C is actually cooling like it should?

If you're low on freon or the system isn't working like it should (heat stuck on for example), you won't ever get to the target temp, or if you do, it'll take a while.

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Current stable:
1995 E320 157K (Nancy)
1983 500SL 125K (SLoL)

Gone but not forgotten:
1986 300SDL (RIP)
1991 350SD
1991 560SEL
1990 560SEL
1986 500SEL Euro (Rusted to nothing at 47K!)

Gone and wanting to forget:
1985 524TD 167K (TotalDumpster™) [Definitely NOT a Benz]