I don't know the history of your particular car, but as most owners of the 124 (at least the ones in the '80s which are in their mid to late teens now) know that there is a blower fan problem witch literally destroys the fuse holder. There is a variety of ways to correct the problem, one of which is to bypass the fuse and install a circuit breaker, along with a new blower motor. This is the route I took over a year ago. When the weather here in NM gets very warm like during the past month, the fan run on high speed with the AC keeps up for about what you said, 45 minutes to an hour, then the circuit breaker starts cutting in and out. On low speed it isn't an issue. My guess is that you have a circuit breaker installed rather than a fuse.

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1996 SL320 97K miles
1996 C220 130k miles
1992 500SEL 170k miles <---sold
1986 300E 216k miles <---sold