Mmmm getting a bit technical! It is good practice and a good idea to unwind and extension as heating does occur when cable has a loading and is coiled up.
However all currents produce some heat and cables should be rated for a particular temperature range. Household flexes and the grey cable used for house wiring are rated at 70 deg C, heat resistant is rated at 90. However, the plug tops and extension sockets are generally not!
Extension leads are sold in 4 main sizes, 0.75mm/1.0mm/1.5mm/2.5mm. These should have different ratings and fuses as the load they can take will be quite different. So when you buy you should ensure that you get one that is rated at 13amps, this is the total loading of the lead so if you have an extension with 4 sockets on the total lead shouldn't exceed that.
Yes roughly 4 amps to a 1000w or 1 KW. Studio lights have some fairly complex electronics, some with multiple capacitors and recharge typically in a very short space of time, maybe 1/2second to 4seconds. There will be a high load therefore for a very short period of time, so if you are banging off one shot after another the cable will get warm/hot depending on the load.
I have run 4 x 750 off one extension without too much trouble but I wasn't using them continuously.
But to return to the OP, running a few lights off one extension lead of the right rating is no problem! If you were running say 4 or 5 lights maybe think about using two extensions.
Hope this is helpful!