What would cause an old engine/transmission to jerk only when not yet hot?

Our car runs great when hot or cold, but until it gets hot, the transmission/engine slips and jerks.
I just drive very slow until engine gets hot, then car runs fine.
Thank you for any ideas.

Please check the transmission fluid level to be certain that the transmission is filled to the correct level. Transmission fluid (oil) expands and flows more smoothly when hot. So, if low on fluid, it may not be filling the valve body and other components, and hence the jerking.
Automatic transmissions today are still “fluid drive” machines even though they are not marketed or called that anymore.
Check your owner’s manual to learn when to check it, hot or cold.
Often transmission dip sticks will have separate markings for “Cold” and “Hot” readings.