Would a hot compress effect under eye/tear trough filler?

A hot compress should not impact the results of your filler treatment. You may want to wait at least 24 hours before using the compress to avoid increased swelling and bruising.

Using hot compresses under the eyes should not affect tear trough fillers. The heat will not ruin the results.

No. In my professional opinion, when getting the tear trough for the under eye area injected you should be just fine to apply a hot compress as usual as long as there is no pressure applied to the treated area. Making sure there is no pressure applied will prevent any possible movement of filler injected. Good luck!