An improved type of temperature probe for sensing applications in viscous fluids requires a real time solution of a two dimensional form of the inverse heat conduction problem. Two finite difference space marching schemes using either forward or backward time differencing, have been formulated to solve the inverse problem for a simplified representation of a typical probe geometry. Numerical experiments have been performed to determine which scheme most effectively solves the inverse problem using simulated measurement data, with and without added artificial noise. The results show that the scheme employing forward time differencing reduces amplification of measurement noise, but requires future time data, causing a slight delay between the time of internal temperature measurement and fluid temperature prediction. In contrast the backward time differencing scheme produces instantaneous fluid temperature predictions but is more sensitive to random and deterministic error. For the envisaged probe applications the forward time differencing scheme is more suitable, as long as the number of future times is kept below a user specified value.