Monte Carlo simulations were used to study the effect of topological constraints of knotted polymers on their theta temperatures. The theta temperatures were determined through two different definitions-the vanishing of the second virial coefficient A(2)=0, and the quasi-ideal behavior of the radius of gyration, similar toN. Prime knots with chain lengths from N=60 to 300 and with crossings from 3(1) to 9(1) were considered. For chains with finite lengths, it was found that the theta temperature determined from quasi-ideal condition of the knot increases, as the complexity of the knot increases. On the other hand, the topological complexity seemed to have no effect on the theta temperatures determined from the vanishing of the second virial coefficient. Also, our simulation results suggest that for chains with finite crossing numbers, as N-->infinity, theta temperatures for all knots obtained from two different approaches coincide and are equivalent to that of a linear polymer chain. (C) 2003 American Institute of Physics.