another tranny question

I am out of town working and my trans. is acting up. '01 auto, 62k miles, stock, no temp gauge for trans. Had been shifting fine, parked, returned, reverse was fine, put in "D" and I thought I was slipping(spinning) in oil or on hot asphalt. It was 102 degrees out. Tach went up to 2000 and slowly pulled forward. Once in 2nd gear it was better but slipped again in third. This continued for several miles in stop/go traffic. Engine died twice when I came to a stop. Re-started easily and of course "slipped" as I got going. I stopped for 30 minutes, (I figured to let it cool down, and I did check trans oil level-which is full). Drove much better, but still not right. I have driven very short trips (running to wally world) the last two days and haven't noticed the problem. But I have been very slow on accelerating.
I have read many posts the last couple of hours on this problem.

I would like to get home Monday-300 miles of interstate. I have read about rebuilts, exchanges, and BTS. I am not far from BTS, but don't want to spend that kind of money unless I really need to. Any thoughts and/or suggestions of what my problem is and is it safe to try to get home?

Thanks in advance!

SPM