Yes, oil does expand when it is hot. This increase in volume when heated is known as thermal expansion, and occurs because kinetic energy
is transferred to the molecules of the substances which causes the the
molecules to move more quickly and increase the spaces between
themselves.
You can see this when checking the oil levels in your car. If you do it when the engine has been running for a while and is warm, the oil levels will appear higher on the dipstick than if you check when the engine is cold. For this reason you should always check before the car has been used to get an accurate reading.
To find exactly how much oil expands, you can use the following equation which calculates the Change in Volume:
V final - V initial = bVinitial (T final - T initial)
It looks complicated, but then physics is not that simple. Luckily, if you want to learn more about it you might want to check out the following website which shows you how to do the calculations using an online calculator: