Theinverseheatconductionproblem(IHCP)isaseverelyill-posedprobleminthesensethatthesolution(ifitexists)doesnotdependcontinuouslyonthedata.Butnowtheresultsoninverseheatconductionproblemaremainlydevotedtothestandardinverseheatconductionproblem.SomeoptimalerrorboundsinaSobolevspaceofregularizedapproximationsolutionsforasidewaysparabolicequation,i.e.,anon-standardinverseheatconductionproblemwithconvectiontermwhichappearsinsomeappliedsubjectaregiven.