Yeah if the bypass is faulty that might do it or if both pipes are toasty right up next to the bulkhead then probaly a blocked matrix, ie limescale/radiator weld that sort of thing. Try a search but I think a mk3 matrix is a straight swap? and not prone to the dangerous leaks of originals.
When I changed the matrix and stupidly :embarassed: replaced the bypass mine was fine but holy did she ever got hot once I got rid of the bypass

3-4 mins before warm/hot then 5mins+ =

beach in Mexico!