The Tynecastle boss also praised paramedics from the Scottish Ambulance Service who took him to the Little France facility for treatment.
And the 53-year-old had welcome news for Jambos fans, predicting a return to the dugout soon – possibly for the away clash with Motherwell in a fortnight.
“I’d like to thank the paramedics and all staff in the CCU at ERI for their care and professionalism,” he tweeted.
Mr Levein was taken to hospital on Monday morning and is now recovering at home.
His assistant Austin MacPhee has taken charge of first-team affairs until he returns.
Mr Levein briefly returned to social media after a self-enforced exile to update supporters on his progress.
“Out of Twitter retirement for a short period,” he posted. “I’d like everyone to know that I’m feeling great and aiming to be back in the dugout for the Motherwell match, all being well.
Mr Levin also reserved special mention for the support he has received from the football community – including rivals Hibs.
He added: “Huge respect and gratitude to the Hearts supporters and those of other clubs (including our friends across the city) who have taken time to wish me well.”
Broadcaster Eilidh Barbour tweeted her support: “Glad to hear you’re on the mend Craig. All the best.”
The Royal Infirmary’s intensive coronary care unit became the first of its kind in Europe when opened in 1964 by Professor Michael Oliver, one of the top heart specialists of his era.
One of the more common procedures performed at the unit is to insert stents – tube-shaped devices placed in the coronary arteries to keep them open in the treatment of heart disease.
The charity British Heart Foundation report that diagnosis, treatment and prevention of heart disease are more effective than ever, attributable to decades of research.
Death rates from heart disease in Scotland have fallen dramatically and yet latest figures show 2,100 heart attack patients admitted to hospital every month, with 560 deaths.
The charity is currently funding over £38 million of medical research into heart and circulatory diseases in Edinburgh institutions. This includes a Centre of Research Excellence at the University of Edinburgh at Little France, next to the Royal Infirmary.
Mr Levein is not the only high-profile figure to benefit recently from treatment at the Royal Infirmary’s coronary care unit.
Former Scottish Health Secretary Alex Neil had a stent inserted after collapsing at Holyrood last year.
Tracey Gillies, Medical Director, NHS Lothian said: “We would like to take this opportunity to wish Mr Levein well in his continued recovery and we appreciate him taking the time to thank our staff.
“We know our staff don’t look for thanks but it means a great deal, especially when it comes directly from our patients.”