94 Corolla Sputtering and low acceleration

What is your question?

94 Corolla after warming up sputters at slower speeds or at stops. No sputtering at higher speeds. The car will eventually stop at low speeds. May restart immediately but get best results by letting engine cool off for 20 minutes or so before restarting.This is escalation from several months ago when I began having to shift into 1st gear to get acceleration from dead stop. Are these two things connected or possibly unrelated problems?

What makes this problem better or worse?

Warm engine and slow speeds

How long has your 1994 Toyota Corolla had this problem?

3 months