The court is expected to make a “reserved” judgement rather than an immediate one, and it is likely to be several weeks before the decision is published.
Aldhouse claims extradition to Thailand would be a violation of his human rights due to the inhumane conditions in Thai prisons.
If his appeal is unsuccessful, Aldhouse will be the first British citizen ever extradited to face trial in Thailand.
British Home Secretary Theresa May had attempted to block his High Court extradition appeal in December last year, but the judges decided his concerns were genuine and his appeal should be heard.
Aldhouse is alleged to have been involved in a drunken altercation with Longfellow in Rawai’s Freedom Bar in August 2010.
He allegedly then followed Longfellow home and stabbed him to death, before fleeing home to the UK.
He was arrested at Heathrow Airport when records showed that he was wanted on an outstanding, unrelated warrant.
After serving the remainder of his outstanding UK sentence, Aldhouse was re-arrested for the murder of Longfellow, a US Marine who served with distinction in Iraq and Afghanistan and was taking time out in Phuket to recover from a shrapnel wound sustained while on active duty.