As you’ve written it, I think hadhad is necessary. It reads off without it.
But re-arranging things, it's not needed.
Standing in front of the sliding glass door, sweating, he remembered last year and stepping into a convenience store.
And, now the statement has some suspense to it. \o/!
I’ve had this argument with another writer, who insists that ‘had’had needs to be used in past tense sentences to avoid the confusion of simultaneous actions. I found it pedantic, and didn’t like how it changed my writing.
For me, I only use had if the sentence needs it to sound right, or if I need to be very clear about the order of events or actions or reaction in a sentence. If a sentence sounds okay without had, and its meaning clear, I avoid using it since its a kind of hard sounding word that throws my rhythms off