Which elimination is this?
An E1 mechanism is highly unlikely. I don't know what level you're at, but one could invoke the Hammond Postulate in this case, and look at the high energy cation intermediate. There are three chloride leaving groups that could generate one of two intermediates. Both of these intermediates are primary cations. A chloride substituent isn't likely to be able to stabilize this much via resonance but more likely destabilize due to inductive effects.

The other potential mechanisms to consider (that do not involve a cation intermediate) are E2 and E1cb. E1cb might work for the first step depending on where the anion is formed, especially if the inductive effect of the chlorines is enough to help stabilize the carbanion. E2 just requires an anti-periplanar arrangement, which isn't hard here with free rotation.

The reason I'd favor E2 and the reason the reaction likely requires heat is the fact that hydroxide is just an OK base. Add to that the fact that it's in a polar protic solvent that might further dampen basicity. If you tried this reaction with an amide base (e.g., LDA) in toluene, I would guess no heating is necessary.

Heating is generally helpful for E1 because the dissociation of the leaving group is slow. However, the need to heat a reaction is by no means indicative that it is E1 (it might not even be an elimination!). Any number of factors could conspire to make the reaction slow, in which case, heating might help make the reaction proceed at a faster, more practical rate.